Sweet but over involved MIL

We just revealed the pregnancy on NYE to my partner’s family, and his mom immediately asked to come to the first doctor appointment. I’m ok with her coming for one, but I need to find a gentle way to limit her presence at the appointments and during the birth.

This is my first, but I already feel strongly about who I want present, which is my partner, my BFF and my sister. Depending on how labor is going, I might be ok with a few people coming and going, but this is not going to be an extended party!

Thoughts? Successfully used strategies to keep feelings from being hurt?