This is really beyond your control, let it go. Your sitter is not doing you any favors by stirring you up.
STBX is not doing anything abusive. He is in what he assumes will be a LTR and has decent living conditions for the kids. Don't ASSume you know anything about who is making what choices. STBX will do exactly what he wants. He is the one screwing up. He is the one making bad choices. Don't put that on his GF. He may even be saying one thing to you and then doing exactly what he wants and assuming he can let GF play the heavy in your mind. His choices with respect to his kids are his responsibility.
Talk to a L if it will help you feel better. Don't bother to rangle with STBX unless you decide with the help of a L to take him to court.
Stick to the custody agreement. Quit expecting favors, quit expecting flexibility. Stick to the custody agreement.
Quit trying to manipulate STBX into doing what you want. It is not your choice to make whether or not he sees the C. Take S10 to the C yourself. If the C thinks it is critical to talk to STBX, she can call him.
Get out of STBX's life. The kids are safe. You don't like his choices, but they are HIS choices. The best thing you can do for your kids is to respect his space. Leave him alone and butt out until and unless there is a genuine concern about harming the children at issue. The C should be able to help you determine whether the emotional harm of a too-quickly blended family is worse than the disruption you want to cause in the kids' R with their father.
And think about this. A lot of your reaction is still grounded in baggage, anger, and jealousy. Consider DBers you know who are blending families way too early as well. I doubt you think they are evil doers recklessly bent on destroying their kids' lives. For your own sake and your kids, you've really got to get some perspective on this.