That's generally my approach as well - concede the point when they come up with something good, but try to slowly introduce new information.
I hadn't heard about the Omicron variant (full disclosure, I limit my exposure to the news - there's little I can do about any of it, and it stresses me out) so that would be helpful.
I did talk about life expectancy with/without the vaccine in my last email to her, too. Honestly, I don't know if it's all an exercise in futility. But my mom listens to this lady, and so do many other hundreds of people. If I can introduce new ideas to her, maybe it will make a difference.
And about your dad, I'm so sorry. Knowing someone you love is in pain (and there's nothing you can do about it) is a special kind of hell, even though it's a normal part of almost every life. I hope you'll be able to carve out some time to take good care of yourself while you're supporting him.