You should come up with a plan to split your finances from your ex, regardless of his current relationship situation is. It's just not a sustainable situation in the long run for you to have your finances co-mingled. And it's better to start the process now (doesn't have to be a sudden/drastic thing) when you are getting along well. If he contacts a lawyer for whatever reason, you could easily end up getting hurt financially in a VERY big way. I would contact a lawyer if I were you, learn your options, and what risks inaction are leaving you open for, and what you can do to mitigate them. And for your kids sake if your lawyer suggests that you screw over your ex, tell them politely that you want to be fair, and not do anything to create unnecessary bad feelings with your ex.

But you want to be the one who is controlling the agenda on how your finances will be separated, you really don't want your ex's girlfriend be the driving force behind this. And face it, it's going to happen at some point, better to control the situation than have it control you.