To be sure, the 1914 issue is going to remain a confused mess because of those interested in this chronology for their own reference, both witnesses, Freemasons and anti-Biblicalists and variations of all three. The discord over this chronology or any usually is an indication of extensive revisionism, which is certainly the case here.
Your other problem is that hard-core witnesses worship the organization more than the Bible and so while they will often discount secular sources which conflict directly with the Bible they will reject the Bible when it contradicts the organization. So what I offer is something on this topic that might not solve your problem, it will show you where 1914 is non-Biblical but will not provide you with the correct dating of the fall of Jerusalem, etc. These would be the points to try out with your mother and not all the secular stuff since some of that is quite dismissible and rightly so and even if other references are reliable they will be prejudiciously dismissed unreliable or even "Satanic". The two points for a witness anti-1914 argument rests thus in these two points I've found: 1) To establish that the 70 years did not begin with the fall of Jerusalem in the 19th year of Nebuchadnezzar but at the time of the last deportation; and 2) Martin Anstey's, et al, determination that the "70 weeks" prophecy should be fulfilled by Cyrus in his 1st year rather than by Nehemiah in the 20th of Artaxerxes. Here's the goods on those:
1) For the 70 years beginning with the last deportation, you've got a great chance if you can get your mother to listen. Mine won't even listen to me and runs into the bedroom when she see's the argument going in the wrong direction; if you don't know about it, you don't have to admit it, right? So be cautious. Note that the WTS quotes Josephus regarding the 70 years. They use Josephus to establish that historically, the Jews understood the 70 years were a period of desolation of the land and exile of the people that was post destruction of Jerusalem and ended with the return of the Jews in the 1st of Cyrus. BUT...JWs misquote Josephus here! Now emphasis THAT. Tell your motion, "Look, the witnesses quote Josephus about the 70 years but they misquote when he begins the 70 years!" That is, the witnesses begin the 70 years when Jerusalem falls, but Josephus does not begin the 70 years until the last deportation. So point out the scriptures:
a) Jeremiah 52:30 says there was a last deportation in the 23rd year!!
b) Josephus claims the last deportation were of those who ran down to Egypt.
c) Jeremiah 44:14, 28 shows those who ran down to Egypt would return to Judea, few in number who "escaped from the sword". Thus the Bible does not contradict Josephus here. It just adds that apparently when they were deported from Egypt in the 23rd year of Nebuchadnezzar, they must have stopped on their way through Judea.
Now here is your Josephus quote since it will save you the time to look it up. It's Josephus, Antiquities of the Jews, 11:1:1. VERY IMPORTANT QUOTE: It is not about the desolation of the Jerusalem for 70 years but the "servitude" of a specific people, the "poor people" left in the land who are now being deported in the 23rd year of Nebuchadnezzar, AND it specifically says this is the fulfillment of Jeremiah's prophecy. So you've got 1) Servitude of poor people , 2) Jeremiah's prophecy and 3) the 70 years beginning the 23rd year, all wrapped up into one. A VERY IMPORANT reference. Your argument/point to your mother would simply be that, yes, 70 years did transpire per the prophecy of Jeremiah, but it began when the last people were deported out of the land and included Jeremiah who had ran down to Egypt and that's how the Jews understand the 70 years and when it began. Thus witnesses misuse Josephus regarding the 70 years who specifically does not begin the 70 years until the last deportation in year 23 AND that is what the BIBLE supports, not the 70 years beginning when Jersualem fell. THEREFORE, 1914, if you are content with the 539BCE dating, is WRONG and needs to be moved back 4 years, to 611BCE, meaning the end of the 2520 years PER THE BIBLE AND JOSEPHUS really more correctly should fall in 1910 rather than 1914.
Now granted, this is still the wrong dating but it does what you want which is it shows that 1914 is WRONG per the Bible, which also begins the 70 years at the last deportation (which is very logical, right?) Further, since they quote Josephus, they validate him, which traps them because he agrees with the Bible that the last deportation began the 70 years. So you can get the witnesses on being both wrong and misquoting Josephus' specific reference to the 70 years. So show this to your mother, here's the quote:
IN the first year of the reign of Cyrus which was the seventieth from the day that our people were removed out of their own land into Babylon. God commiserated the captivity and calamity of these poor people, according as he had foretold to them by Jeremiah the prophet, before the destruction of the city, that after they had served Nebuchadnezzar and his posterity, and after they had undergone that servitude seventy years, he would restore them again to the land of their fathers, and they should build their temple, and enjoy their ancient prosperity. And these things God did afford them; for he stirred up the mind of Cyrus and made him write this throughout all Asia "Thus saith Cyrus the king: Since God Almighty hath appointed me to be king of the habitable earth, I believe that he is that God which the nation of the Israelites worship; for indeed he foretold my name by the prophets, and that I should build him a house at Jerusalem in the country of Judea."
Now please note again, this is only half a rebuttal. It proves 1914 is wrong by the witnesses own miscalculation of when the 70 years began, regardless of the fact that they might have the wrong dating for the fall of Babylon. But this argument allows you to avoid all that confusion and distraction of the dating issues. That is, you don't have to argue 539BCE is right or wrong (even though it's actually wrong), you're still presuming that 537BCE is the right date for the return of the Jews (even though it's wrong), and you are still agreeing that the Bible insists upon 70 years of desolation of Jerusalem sometime after the fall of Jerusalem. The only thing you are disagreeing upon is that though the WTS quote Josephus to support this was a literal 70 years, they misrepresent exactly WHEN Josephus begins the 70 years and that Josephus' beginning of the 70 years is more consistent with when the Bible dates the 70 years which is at the time of the last deportation and not the same year as the fall of Jerusalem. This proves 1914 is WRONG whether or not in the next 50 years you ever figure out what the true dating is. So that's the beauty of this argument, Bible vs witness, there is no way out.
2) The "70 weeks" prophecy fulfilled by Cyrus. Now you might not feel comfortable with this challenge. But basically you can note that some Biblical scholars, like Martin Anstey, believed that Cyrus was supposed to fulfill the 70 weeks prophecy and thus the 1st of Cyrus should begin in 455BCE. This is pretty basic. You might just remind your mother that the prophecy was to begin when the "word goes forth to rebuild Jerusalem" and that the Jews obviously began to rebuild Jerusalem in the 1st of Cyrus so he would easily fulfill this prophecy. However, that probably discrepancies in the dating for this period has forced trying to make this fulfillment to 455BCE work with some other event relating to the temple. At this point, you can merely say, "Mom, IF in fact there were revisions in the chronology, which Jehovah's witnesses presume is the case because the pagan chronology contradicts the Bible often, as in the case of the 70 years, then it's possible that 539BCE is also in error. Some believe that Cyrus' 1st year, therefore, should be dated to 455BCE in fulfillment of the prophecy. IF on further investigation, Mom, this is the case, that 539BCE is wrong too as the witnesses claim the fall of Jerusalem in 587BCE is, or the 20th of Artaxerxes in 445BCE is, then 1914 would be wrong also." Of note, the 539BCE chronology is quite embedded and part of the 587-539-445BCE chronology for the fall of Jerusalem-Fall of Babylon-20th of Artaxerxes. So if the witnesses are going to cast out 587BCE and 445BCE for unreliability then it makes 539BCE suspect as well.
Now you can leave it at this, and I suggest you do, simply suggesting that Cyrus actually fulfilled the prophecy. Once you plant that idea in her head and she starts thinking about it, then it will grow and make her wonder and if she investigates further she'll probably come to the conclusion on her own that the BIBLE itself, which in Isaiah says specifically that Cyrus will rebuild BOTH Jerusalem and the temple, then this is why some believe that even 539BCE is a wrong date per the Bible!
Now don't take sides here. Just establish that there is a "possibility" that 539BCE is also incorrect and that Cyrus actually fulfills that prophecy. Nothing in the Bible will contradict that. This establishes that actually the WTS relies on secular history's 539BCE date rather than the Bible, so you've got another Bible versus secular history "idea" going. This will not solve the issue but will put REASONABLE DOUBT onto the matter, especially since item #1 doesn't work for 1914 and proves it is absolutely wrong based upon a mistake of false calculation.
That's it. If you try to argue WHY 455BCE for the 1st of Cyrus should work and why Nehemiah's 55-days of rebuilding the wall around Jerusalem doesn't then that's a lot of talk and discussion and you need lots of expertise and when you lose one little point then the discussion usually ends. This simply alerts your mother to CYRUS needing to fulfill this prophecy and that 539BCE is considered a wrong date by some who believe the Bible and that they dismiss ALL the pagan chronology which they believe to be revised, instead of just 587 and 445BCE as the witnesses do.
And again, even though this doesn't establish what the correct dating is (even though 455BCE is now proven by the VAT4956 to be correct), it certainly throws enough doubt on the 1914 issue, sufficient enough for a "reasonable person" to reject it as being Biblical until further investigation.
These are points that are easy to focus on and does not involve a lot of interpretation or arguing and will make your mother THINK. One argument disproves 1914 absolutely another recommends a better translation which would also disprove 1914, but in the end it makes 1914 a date that can be reasonably rejected based upon the BIBLE! Remember all your arguments now are pro-Biblical! The idea is not to debate on the plane of JW vs pagan chronology but JW vs the Bible, or their own misquoting of secular sources (i.e. Josephus).
Let me know what happens!!!
But I'll tell you now, in my experience, if she is a true J-dub, even if something is clearly shown to her in the Bible where the witnesses are wrong, she will reject even the Bible because to her, there is no truth that does not first come from the Watchtower. I've had some tell me that I may indeed be right, but it's not their responsibility to respond to it unless it comes from the organization first. Thus they are trained to "follow" and not "run ahead" of the organization, so may still fall on deaf ears.
But just maybe, if your mother is truly a "Biblical-witness" at heart, and realizes that the society sometimes has to change and update things (which is they long history!) then this just might be something else that is wrong that they may eventually have to change. And then that "seed" will grow. She will then begin to question other things that don't quite fit the Bible and soon she may realize, even with the help of holy spirit, that the Watchtower organization has been abandoned spiritually by Jehovah at this time and it's time. This "process" is the individual decision to "leave the broad and spacious road" and seek the "narrow and straight road"--that is, direct Biblical examination and search for truth, using it to examine everything including the JW doctrines!
You have my best wishes!
JC