How would you deal with this kind of circumstance?

My older daughter has mental health issues. She calls my other daughter and my ex and tells them things she has merely imagined. She can take a situation and her brain switches it into things that never happened or that never were said by me. It’s very upsetting when it happens and my ex and daughter look at me with suspicion when wondering if I ever said or did such things. I am defending myself but they may think, without proof, that “mom is really nuts.” How can I keep this from bothering me so much or do I have to just learn to laugh it off? It’s been going on for years and there’s no reason to believe it won’t keep happening. This is a person who tells people she hasn’t seen me in three years but last year we drove for four hours and took her to a restaurant. She doesn’t remember it.