Hithere
Her daughter her rules
There could be a reason why your dd wants a cam, maybe it is the first sleep over and dd or gd is anxious
Not worth fighting it
Seriously? No room for negotiation? In the OP’s own home?
I think that this needs a conversation if possible. If the child is happier knowing she can talk to her mum, for instance, that would put a different slant on things.
Nicolette, can you suggest that the camera is only switched on when your granddaughter is alone in the room? That way, there is no question of you being monitored (I would strongly object to that!) and the arrangement would be between your daughter and granddaughter.
I think it sounds very unhealthy, but ultimately it is your daughter’s call. Where you come into it is that it is your home, and I think that you do have a say about what happens there. You do, however, need to be prepared for being told that it’s your daughter’s way or the highway, and have decided what you would do if that happened.