Oohhh no.
Its fine to bath with your GC IF you have asked the parents permisson and thats all ok in your household.
We had an incident long time ago where my DD " disclosed" that granny used to get in the bath with her"!
I was on the floor - astounded.
It was way over stepping boundaries but like you op, we just could not be sure that this actually happened.
If it did, I am not happy about it - but in my case fits with the same controlling, posseive maddness.
Op, we " exposed" our DD to her Gm for a long time, like you we thought, I thought.....its good for her to have regular contact as she has nothing on my side.
I have now totally changed my mind.
My DD never ever warmed to her, has only just started too years later. she never came back in a good mood, always quiet and shy and reserved, they never brought her on in anyway at all, no activities, or anything, they never took her anywhere - except local play park,....
it was all about MIL wanting to be in charge, be the star and serve her food.
We haver totally cut down contact now to a few times a year.
It used to be several times a month ( but never enough for her).
Even then, they use their time to ask mummy to ask if you can come back tomorrow, why don't we see you more, and now DD comes back sad.
I don't get on with them, they have been horrid to me and to DH, we had to say - why are we putting this small child who us used to us and our way of doing things, with a woman whom we both have major issues with?