When he says your family, does he mean only your child, or is he referring to others?

I wouldn't like his style of giving you the ultimatum. You can assume this is the first of many.

I read your other posts. Is it possible he moves in so quickly because he uses women for a place to live? Is that why he's giving you the bum's rush?

Stick to your guns. Protecting yourself and your child is #1.

I'd discuss negotiating tactics with him and how I didn't like the pressure and nip that in the bud. I hope you can work things out and he is worthy of meeting your family and being part of your life.