Oh, and I forgot to add: Arguing about sonograms makes BabyJesus cry 
I didn’t have any sonograms - my dr didn’t see the need and neither did I. Plus I wanted to be surprised by the baby’s sex. But I don’t think I’d have minded if my mother or MIL came along.
Witnessing the birth, however, would be an entirely different story. My husband was the only non-medical person present, and that’s how I wanted it.
Speaking as an employee in an OB GYN office…
We have patients bring loads of people to their sono appts; mothers, fathers, siblings , friends, children etc. Our sonographer had to put a limit on the number of people in the room. (It’s 5, BTW)
No fuckin’ way. I like my MIL just fine, but that should be a moment for just you and the ol’ man. But you’re a nice girl for humoring her.