Your ex moved on to his new life aleC4, and like mine and no doubt countless others was so wrapped up in his own happy bubble that he really thought the kids would be happy too, because dad was happy.
Mine did this. My three kids were teens when it happened, so thankfully there was no staying with him to negotiate. From the start they decided when and if to visit, which for our youngest lad at 13 was never, because he didn't want to see his dad in his new home with his new partner. It was simply too much for him to handle. There was, and still is a lot of anger in my son, now a strapping twenty year old. He still sees his dad at a neutral place.
I've said it before, but it might be worth repeating: there is a price men like our exes have to pay for blowing their family apart. That price is what is causing the anger in him now.
You see, the honeymoon period has worn off, and he is dealing with reality, and it isn't the rose coloured version he imagined. Your DD is angry and resentful. Too young to analyse and articulate it, she's naturally happier with mum in the family home where she feels safe. Your ex should rise above this, accept that he's the adult and accept too the blame and fallout for his actions. But that would take guts. So, like my ex he's getting angry in return. It's the easier option for them, because the alternative is too much for them to bear.
He wants to play happy families with his kids, her kids. He needs his kids to be happy round him, because it makes him feel better about his selfish choice to start again. He doesn't get that he had a happy family, and he blew it. Well he does, but he's buried that deep inside, because it's too painful to acknowledge.
Because we live with the kids day in day out, we know how hard it is for them to adjust. They didn't want this any more than we did. But because we're a close unit we forge ahead and make a different but happy home. He resents this, like my ex he feels that he should dip in and out as he chooses, because that's his right. He feels he shouldn't move heaven and earth because he's their dad, they should want to be with him for that reason alone, end of.
They gloss over their kids devastation, because to try and unravel it, and fix it would be like holding a huge mirror up, reflecting their incredibly entitled behaviour.
In a year or two your DD will decide for herself if and when and on what terms she sees her dad. He can't assume how she feels and he can't control how she reacts.
For now I would put staying with him on hold. He took a gamble when he left regarding his kids. Loved up and thinking he was in the right he mistakenly thought they'd want to be with him regardless.
Take their lead, you owe him nothing. If DD doesn't want to stay, then don't make her. He will blame you, I got blamed for DS countless times. He'll blame you because again, he can't or won't blame himself. So be it. Shrug it off, make sure your kids are ok. It isn't up to you to facilitate a relationship between your kids and their father. That's his job, and his alone.