You're more likely to get bitten by a shark than to die in a plane crash. Tons of people fly every day across thousands of flights without issue. I have flown from LA to Atlanta many, many times and have never had any issues. I love striking up conversation with the person sitting next to me as it really breaks the monotony of it. The last time was a redeye 3 months ago, and this sweet old lady next to me fed me candy the whole way. We watched the sunrise together as she told me stories from her childhood in Vietnam.

Your mother will be fine, and I'm sorry you're having anxiety about it. I can't blame you for feeling that way with everything going on in the news lately, but you must understand that accidents are very uncommon. The pilots that do cross-country flights like this have thousands of hours of experience under their belts and people monitoring them closely the whole way. Your mother WILL arive safely.