Yes they do act like a couple three different people. It's all a part of it.
My wife just left a few minutes ago. She was flirting with me hard. She reminded me of a school girl. I flirted with her back, but I had a cocky edge to myself, kind of like a careless type of attitude.
Don't get sucked in man. It's a CRAZY back and forth dance. The part about her mentioning breaking up after she just invited you to do something is a button push, she wanted a reaction. Mine tried this today too. I just started joking with her and acted like I didn't care.
Hang in there man, yes you have to look out for yourself, but at the same time you can't make them aware of it.