Can I just add I think your MIL actually sounds lovely and like she means well. She sounds very excited about the birth and at the same time she wants to hang on to her wonderful bond with her son.
I have a good friend who married a man who was very very close to his mum. In the end it didn't go well because she never knew when to butt out and when her help was wanted. She was overbearing but I think she always meant well. The problem was it undermined her daughter in law (my friend) to the point she never wanted her MIL around.
You should be able to have a good relationship with your MIL but you need to get it off on the right footing before the baby arrives and keep working on it after the baby is born.