Rachel, just want to offer my support and let you know I'm sending positive thoughts and vibes your way.
He's acting VERY immature and I'll be honest, this type of behavior hits very close to home for me because my first husband (ds's bio Dad, he's been adopted by dh now) did the very same things to me. He eventually cheated. Not saying that is where your relationship is headed, just that you are doing that right thing by staying right on top of this and letting him know how you feel. When something feels "off" - it is. My very best advise is to never ignore your instincts or let him talk you out of them.
I'm so very sorry you are having to deal with this on top of the pregnancy and two very young children. I really, really hope your dh can grow up and realize that his family is worth so much more than the attention and flirting with some random lady.