As others have said, you and DH need to, first of all, have a discussion. Tell him what is making you feel so uncomfortable, and pressurised, and let him say whether he feels you are justified or not.
If he agrees with you, then he needs to present a united front with you. His first loyalty should be to you, if justified, regardless of whether it might upset his mother or not.
When you are both in agreement with the way forward, so that you feel more relaxed and happy with the relationship between her and your daughter, then have a JOINT calm talk with MIL.
She sounds overbearing, although that could just be the way you are seeing and portraying her. But, grandparents are the supporting act in a child’s life, not the star turn, and parent’s wishes come first.
So, no lists of rules, texts, emails or letters to do this, (or worse a generic print out from the net!), a calm voice conversation would be best.
Tell her how she’s making you feel, listen calmly to her response, and try to find a way forward. She may not know she’s upsetting you, but at least give her a chance to modify her behaviour. The “mummy” name thing is a complete no-no, in my view.
If it ends up in tears and tantrums from her, then still press on calmly.
Time alone with GC should evolve naturally - no demands or regular requests need to be made. My children adored my parents, they stayed with them, they holidayed with them, and that was fine. No one had any worries about boundaries. Same with my grandchildren, life just evolved, as time went on.
It really is best if these issues could be ironed out calmly, before it kicks off into a huge row - estrangement makes very few happy, and both sides end up losing. (Unless, of course, there are very good reasons for it.)
If she doesn’t, after a chat, respond to this, then I guess you will need to firm it up, and actually lay down the law a bit.
Your daughter is the child of you and your husband, and, in the end, you have the final say.