DD is three, and getting more and more able to understand how people are behaving. MIL is pretty manipulative and unpleasant, and she doesn't like me at all. DP recognises that MIL frequently behaves badly, and does generally make some effort to call her on it (though I think she could probably do more), but also, DP is human and it's her mother, and she loves and misses her. It's fair to say MIL also had a pretty shit life and there are ample reasons why she'd be as she is.
Describing a recent visit would give you some idea of what she's like. We went down just after the guidance about visiting family in their home changed. DP explained to MIL that we know a lot of people (including my parents) who are still very anxious and, out of respect to them, we really didn't want her to be hugging DD or picking her up/kissing her. I know it's hard, but MIL immediately picked her up, wanted her to hug everyone, kept going back for more, and whenever we asked her not to she'd say 'it's fine, it's only family' or 'she's going to be very upset and confused if you don't let her'. During the same visit, SIL (MIL's other daughter) was there with her son; MIL persistently criticised his eating habits and his screen time to me, telling me 'you brought up DD properly, none of this'. Obviously we demurred, and SIL is pretty patient with her mother.
But, it was obvious DD was beginning to recognise some of this behaviour isn't normal. She has asked me 'why doesn't granny like you' a few times, and 'is granny angry with [cousin's name]?'
We had a short, very simple chat about 'granny is sometimes a bit funny and you shouldn't worry too much,' but TBH I do worry. I have already reduced contact as much as seems fair on DP, and I have to admit she can on occasion be lovely with DD.
The only times I've directly challenged things, MIL has either burst into tears and required everyone to comfort her, or insisted she never said or did anything wrong.