You clearly don't actually have any intention of changing anything so why even bother yourself about how your DD feels? You want this relationship, she doesn't have to like it, or him, or play nice and sweet and play happy families. Or is it more that you don't want your poor bloke feeling put out by her behaviour?
I'm not being an arse for fun, it hits a sore spot when I hear things like this. I was forced to 'like' my mothers boyfriend when I was young and be nicey nicey to him. I could sense something wasn't right and I didn't like him from day one. He eventually cheated on my mum and physically abused me. I'm not saying your new man is an abuser but you've not been seeing him long and if there is something wrong that you can't sense, he won't let it show yet. Are you sure you can really see the red flags if there are any?
If you're really in it for the long haul, wait til DD moves out before you move him in or anything. Don't make the poor girl uncomfortable in her own home, or uproot her to move for this man.
You sound resentful to your kids for staying in your poor marriage before. I have sympathy for you that your ex was awful, but don't try pin it on them. If she doesn't like him either, you obviously weren't staying with him for her sake and shouldn't use that as an excuse. You stayed despite being unhappy. Do they even know how you felt? If you do tell them, don't use the 'I did it for you, now let me be happy' card and guilt DD into accepting this man.
Sorry, OP, but I've been the DD and I would just think carefully before making any big decisions with this man. Please just think and use your head. Don't be overwhelmed and blinded by the attention and affection you were missing before.