Well your mother isn't acting very Christian like at all for a start. Her way of converting you is to use scare tactics and fear? More importantly she has no idea and cannot prove that she will be saved.
One thing is on your side and that is time. Tell her straight that one day you will be next to her as she lies on her death bed. Warn her now that she will die, of old age because Armageddon will not come.
I personally would point out that Matthew 7:1 warns Christians "Do Not Judge, or you too will be judged". Your mother is judging you and that goes against the Bible.
Matthew 24:36 - The Witnesses predicted the time of the end many times. This is scripturally impossible so WHY did they do it?
"No one knows about that day or hour, not even the angels in heaven, nor the Son, but only the Father.
Deuteronomy 18:22 warns of False Prophets.
If what a prophet proclaims in the name of the LORD does not take place or come true, that is a message the LORD has not spoken. That prophet has spoken presumptuously, so do not be alarmed.
By those terms, the Watchtower Society is itself a False Prophet and therefore her message/the word of the Watchtower and its publications is to be ignored completely. They predicted that events would happen and were wrong. This scripture does not say anything about motives, so whether or not the Society were genuine doesn't matter - they are false prophets.
Two scriptures in Luke warn against groups like the Watchtower Society who continue to warn of signs of the end, obsessing over them rather than focusing on the important things.
Luke 17:20-24
20 Now having been questioned by the Pharisees as to when the kingdom of God was coming, He answered them and said, “The kingdom of God is not coming with signs to be observed; 21 nor will they say, ‘Look, here it is!’ or, ‘There it is!’ For behold, the kingdom of God is [b]in your midst.”
21 nor will they say, ‘Look, here it is!’ or, ‘There it is!’ For behold, the kingdom of God is [a]in your midst.”
22 And He said to the disciples, “The days will come when you will long to see one of the days of the Son of Man, and you will not see it. 23 They will say to you, ‘Look there! Look here!’ Do not go away, and do not run after them. 24 For just like the lightning, when it flashes out of one part of the sky, shines to the other part of the sky, so will the Son of Man be in His day.
Luke 21:8 - The Society claim to be God's mouthpiece, his channel and in a sense God himself on earth.
8 He replied: “Watch out that you are not deceived. For many will come in my name, claiming, ‘I am he,’ and, ‘The time is near.’ Do not follow them.
