Your mom got the doctrine right. According to JW doctrine, before 1914, Satan was allowed to roam freely on earth and on heaven. But 1914 marked the end of the gentile times, and thus Christ was put in power in heaven, and his first act of power was to kick Satan out of heaven and confine him to the earth. This is all in Revelation, chapter 12:
5 She gave birth to a son, a male child, who will rule all the nations with an iron scepter. And her child was snatched up to God and to his throne. 6 The woman fled into the desert to a place prepared for her by God, where she might be taken care of for 1,260 days.
7 And there was war in heaven. Michael and his angels fought against the dragon, and the dragon and his angels fought back. 8 But he was not strong enough, and they lost their place in heaven. 9 The great dragon was hurled down--that ancient serpent called the devil, or Satan, who leads the whole world astray. He was hurled to the earth, and his angels with him.
10 Then I heard a loud voice in heaven say:
"Now have come the salvation and the power and the kingdom of our God,
and the authority of his Christ.
For the accuser of our brothers,
who accuses them before our God day and night,
has been hurled down.
11 They overcame him
by the blood of the Lamb
and by the word of their testimony;
they did not love their lives so much
as to shrink from death.
12 Therefore rejoice, you heavens
and you who dwell in them!
But woe to the earth and the sea,
because the devil has gone down to you!
He is filled with fury,
because he knows that his time is short."
So these events marked the beginning of the "last days of this system" and one of those signs was WWI. You don't really need to refute this using bible passages since the whole doctrine is based on the interpretation Daniel 4 of the seven times prophecy which equal 2520 years counted from the start year of 607 bce which is, according to the wts, when the destruction of Jerusalem by the babylonians. So when you add 2520 years to 607 you get 1914. Of course, many people here can provide evidence that clearly shows that 607 was not the date when the babylonians led by Nebukadnetsar destroyed Jerusalem, but in fact Jerusalem was destroyed in 586/587 bce which means they're date is off by 20 years. So just tell your mom that Satan couldn't have been sent on earth in 1914 because the destruction of Jerusalem was in 586/587 bce NOT 607 bce as the JW claim. You can even prove it to her using the society's own writings. Farkel made a thread with a very easy method where by using the wts' own publications you prove that it was impossible for the destruction of Jerusalem to be in 607. I'll look it up.
P.S. edited to add the link to the thread Farkel made on the subject...enjoy!
http://www.jehovahs-witness.com/12/74549/1.ashx