You handle things by being an assertive adult and telling your mother/family what the expectations are. Tell her flat out the reasons why you are hesitant at having them at the hospital. Emphasize that you want your privacy respected, especially when it comes to Facebook posts/pictures.
You can't expect people to behave in the way you desire if you never make your desires perfectly clear down to every detail. You cannot just say "please don't make a scene", you need to describe what kind of behaviors you think will make a scene or cause embarrassment, etc. If you don't believe that she/they will respect your boundaries, then do as you suggested and don't call anyone until you're almost ready to deliver.
If you think this problem will go away once baby arrives, think again. Overbearing parents don't stop being that way once the grandchildren come. . . they get worse. They will try to undermine your parenting skills, etc. So you need to set the tone that you are the boss of this pregnancy and your child now, while you still have a chance.

