'He says I'm his soulmate and wishes we'd had a family together. I say we still can but he says his daughter will be too upset. So at least he's putting her needs first.'
No, he's hiding behind her. He's not putting her needs first. The whole soulmate business is a sop to keep you happy. Same with the regret that you two don't have a family together, and the business about his feelings that his first partner wasn't right for him and a pity that he had children with the wrong woman. You want to wish this child away and he has got your measure by calling you his soulmate - magic appeals to you obviously.
He is hiding and throwing you cliches. He gets mad when you suggest keeping his children apart from you at weekends. You have already had one split up because of your issues with the children. You are driving him away. He will choose them one day, or you will 'win' him and he will abandon them.
I don't buy the sudden concern for any problems this child may have. The reference to the teacher's input came very late in the day imo.
'He wishes he hadn't had children with her, although of course doesn't regret having the kids.'
He is rejecting half of her DNA all the same, when he says this. The child of a father who regrets having anything to do with her mother will feel a lot of conflicting loyalties and will be acutely aware of the winds of rejection and negativity swirling around her. If you find some comfort in this sort of statement from him, you are revealing some jealousy of the child's mother. You cannot wish the mother away from the rosy picture either; despite the faults you enumerate, she is the mother of your DP's DD.
I suggested that you were jealous earlier, not of her mother, but of her, as a female with a rival claim on your DP's affections. You seem able to accept that his son has a claim on him and presumably he pays attention to his son while they're together. But woe betide the girl for having a claim on him.