The 'silent treatment' is emotional abuse. Ask him if he'd be willing to go to couples therapy to work on communication during conflict that isn't abusive.

My husband, back before he was my fiance, used to give me the silent treatment. I let him know it was abusive and we had plans to go to couples therapy (that ended up falling through as we were both so busy!) but we were able to talk about it like mature adults and if we are too upset to talk, we let the other person know that we need time alone - communicating our needs that we needs to cool off, and also insinuates that yes, we will talk about this later, and then we do. If he refused to stop being an abusive asshole and chose to not grow up emotionally, we never would have made it.

When women are uncomfortable, it can stall labour. This is one of those times when you're allowed to ignore his needs - you're bringing a child into this world! If she's not baby-sitting your son, where is he going to be? It's a scary time with new things and changes, and he'd probably prefer being with grandma instead of with a baby-sitter. Your husband is a grown man who can grow up and be a supportive birth partner without his mommy present. Your son is a child and shouldn't be given the shaft because your husband refuses to stop being a whiny resentful man child.

I am SO UPSET reading about petulant idiots who give the silent treatment - it is abusive and manipulative, so that you question all your decisions and chase after them, making all compromises and giving them all the power because they feel entitled to get what they want or else. I am SO MAD for what he's doing to you. Stand your ground, let him know abusive behaviour is NOT OKAY (is he going to pull abusive shit on your children too?!) and see if there's a couples therapist who can accommodate you quickly. Also, your husband cannot bring his mother to couples therapy appointments either.