I love my MIL but we went through a rough patch after dd was born. One boundary I set that I found helpful was no more three way group chat (me, dh, mil). She kept messaging there and dh cba to reply straightaway and so I had to reply to be polite, even though I was annoyed with her about things she'd done/said about dd. It was weird because fil wasn't on it, my mum wasn't on it, it was just me, dh, mil. Even stuff like "how are you both, how's your weekend, when can i next come visit" would always be on that 3-way chat. So I said to dh, all correspondence from now on must be through you, on a 1-1 chat. Similarly my mum and I have a 1-1 chat and she "books" all visits through me.
It helped a lot and mil's attitude changed in general, she slipped out less snide comments about my parenting when we next met...I think she just needed that reset/reminder, I'm not her daughter!
We get on pretty well now on the whole.