- left me to be with OW - introduced her to S2 - brings her to my house for child handovers - moved her into his house - has her involved with every visitation
As U mentioned - it could be much worse. Your H is showing you some respect (even though he is being insensitive).
I think you can stick to canned responses if you feel your emotions might get out of control.
- I am not comfortable with that - I respectfully disagree with you - I understand your point of view but I don't feel the same way - My only concern is D4's emotional wellbeing
At the end of the day, all you can do is make your point and the let the chips fall. You have no ethical, moral or legal recourse to prevent him from introducing his GF to your daughter.
Avoid anything that implies his relationship isn't serious, that you don't trust his judgement, or that he doesn't have D4's best interests at heart.
This is, by far, the worst part of our situations, but unfortunately it's just another lesson in letting go of control.