Hello. For what i's worth, I have a perspective from both sides.
My xp left us 3 years ago. He met someone else immediately (didn't leave me for her as such, so slightly different situation, but he met this woman 2 days after we finally decided to call it a day - we were still living together, but he virtually moved in with her the night he met her). He introduced her to DD behind my back (she was 2 at the time) & I was furious. Like you, the thought of her cuddling her, tending to a grazed knee or - horrible thought - bathing her or her getting into bed with them - was repugnant and so upsetting.
However, 3 years down the line, xp is married to this woman, and they have a child of their own - ie, a sister for DD. She goes to stay with them reguarly & her step mother is a really important person in her life. BUT, she knows that I am her mum, and step mother is her step mother.
She is really good with DD, and very respectful of my rules, boundaries and the way in which I bring her up. So basically, everyones relatively happy now. Boring cliche, but time is a great healer. I know it's not something you want to think about at the moment, but I think forgiveness is crucial in developing a healthy situation for your DCs in the future.
My other perspective is that I have just met a man who's going through a divorce & has a DS. We are going for our first sort-of-date on Friday with our respective DCs. Now, I expect the DS's mother would be as horrified as I was. But I guess from his point of view, he comes as a package with his son, as do I with DD, so we may as well know where we all stand & see whether we all like each other from the start. My own experience makes me determined to be as sensitive as possible, to respect his space and the sanctity of his relationships with his parents. I have no idea how it's going to work out, but I want to do as I would have liked DD to be done by IYSWIM.
I hope it works out for you almostmidnight (and everyone else). Good luck