The 1919 argument is very well presented in the book, "Captives of a Concept"
I highly reccommend you read it. (I know, everyone is saying, "read this!" but for me, at least, it was the best analysis I have read on the underlying doctrinal basis for the WTS's very existence, and how it can be easily debunked--a real eye opener, even to someone who has done plenty of research on the WTS)
Also, the author presents his experience with a fellow elder who said essentially the same thing your mom did, "if the Witnesses were wrong then God didn?t exist."
Unfortunately, in his experience, this was a sign that the person was not open to reason. But one ray of hope is that you may perhaps get her to teach you the reasons why Jesus and Jehovah chose the WTS as Jehovah's sole channel to mankind. With your help, your mom may learn something new (and damaging) as she is trying to teach you something about the WTS. The book makes reccommendations on how one might accomplish this using the WTS's own history book, "Jehovah's Witnesses, Proclaimers of God's Kingdom".