Hello LittleDipper

Welcome !
I am sorry to hear that the relationship with your mum is strained. I can relate, my mum is BPD / dad NPD. I also have a 9 year old daughter.
I am separated from the dad of my child. I don't know which 'label' to stick on him, and maybe labels don't always matter. But his behavior is sometimes odd. Needless to say, the behavior from my parents also is (or was, since we are NC now).
My initial approach was to make up excuses for odd behavior. Especially when it was about my child's dad - I didn't want to talk badly about him. But now I so much agree with Zachira's viewpoint. Especially since I'm a child of BPD/NPD myself, I know that children tend to take the blame for the behavior of people close to them. So I told my child that yes, sometimes behavior of grandparents and dad is strange and no, it has nothing to do with you. I was at loss at how to explain it, because sometimes she felt hurt by things her dad did. So I told her, well, your dad loves you very much, but something in his brain makes that he sometimes reacts differently then most people. That may have sounded harsh, and it shocked her at first. But I think it also very quickly made her see that well, this is the situation, and we deal with it. No point beating around the bush for me. I also told her that we all have our things in live, and everyone has issues, not only dad. And that the most important thing is that he loved her. (Mind you I didn't tell her this last thing about her grandparents, since I am not sure they love her. No need to make up stories)
Since than I have the impression that she has been feeling better. She realizes that it's not her and secondly, that she cannot change the situation.
I also teach her boundaries, we sometimes roleplay on how she can react when dad says or does something that is a bit strange. She needs to feel that she can protect herself when I am not around.
I don't know if this makes sense to you ?