Sounds to me like he's sensing your detachment and is trying to suck you back in with what he thinks you want to hear, i.e. trouble in paradise.
Now stop for a minute and think about why he would do this. Is he inviting you to resume your usual doormat position and fight for him again, since the new relationship is less rosy? If so, it's all about him, you are merely a bit player in his ego-drama.
BB is probably mental because he is constantly talking about you and how guilty he feels, etc. She has probably unconsciously picked up the competition vibe and will be bad mouthing you constantly, ensuring that she is the winner in the battle for his luurve. I'm sure he has probably intentionally told her that he still has feelings for you, to get more attention from her. He's a sick man.
BB wants your children because she is threatened by you and your unique relationship with your ex-tosser. She knows that she can't compete so wants to join in. Again, nothing to do with the welfare of the kids whose life she has assisted in destroying, but all about her competing with you.
Get the lawyer, sort out the money, get your solicitor to specify no contact from either of them, all contact should be through solicitors. Then eventually let your kids go and stay with them. A few nights with bewildered, demanding, mummy-missing children will piss all over her cornflakes, especially if she has none of her own. Do not underestimate how hard and stressful it is looking after someone elses children, and trying to look good while doing it. She won't be able to complain to ex-bastard as she will be trying to prove to him how good she is with kids. Oh the pathos.
Sorry for the essay, you probably think I'm talking shite but you seem to be so lovely while your shape-shifting ex-bastard and the insecure BB are such a living cliche that it can only end in tears. Though not yours. You'll be one of these wonderful women who move on to an even better life and look back at their ex with a shudder of horror and relief that he is gone.