I saw a post exactly like this on Reddit you should look into it, it might give you some relief seeing all the comments
r/JUSTNOMIL
My MIL is like this. Saying things like “your lovely blue eyes. must be from your grandma” To which I’m like… no? They’re from his mum? Hello? Stands and laughs when I’m comforting him saying I can’t do it that way. Just hideous. You’re definitely not being too sensitive. It’s awful. And people like that are very hard to stand up to. Hopefully your partner offers you more support with it than mine does!
Not being too sensitive. I think you should talk to your MIL, or get partner to do it if you think that would be better, and set some clear boundaries. Just try to make sure you don't make it sound like an attack on her if you can. Lots of "i know you are trying to help and I appreciate it, but" type of stuff.