Is she asking to know where the main home will be, and where any vacation destinations will be? This would be normal in my agreement. My exH is similar to they way you describe the BM in your situation. So, I give him the basics, but not the details. My agreement says I cannot forbid the kids from telling him where we are at any given time, but I have a text from him saying that he has people watching me/us/friends, so I have over-ridden that until a judge tells me that I can't. I think your predicament sounds similar. Basic residency is normal, but going to a restaurant, zoo, etc... seems over the top in high conflict situations. No judge will expect you to tolerate stalking.

What does his agreement say? I don't have child care, but I will say that all school information and contact is available for both of us.

Sounds petty. Good Lord. Sometimes you just let something go. She needs to let this tube sail off to sea...

No parent can force another household to punish a child for any reason. So if she is requesting that, you absolutely don't have to agree whatsoever. However, I don't agree with your namesake. As a step-child, ex-SM, and BM - I only agree with a non-biological parent to be called that when the biological parent is no longer present due to death, adoption, or choice. But the child should not be punished for any reason. I actually have a hard time believing BM is even requesting that. I do understand her being very upset. I was in my SD's life since she was 2yo also. The idea of her calling me mom, or some form of mom would never sit right with me. She has a mom. Do you really feel it's right for another woman's child to call you any variation of mom? As a BM, I can tell you that it would absolutely break my heart if my children referred to their dad's gf as a mother figure. It's a special name, it's a special bond. I hope you will reconsider this.