I hope her Dad pulls you up when you speak of your sons as "ours" but of his dd as "hers". I hope you don't talk about them like that around your sons or his daughter. I really hope you don't treat her as differently as you speak.
I'm projecting here but you sound like my stepmum, she didn't think of me as my Dad's child either, her behaviour and attitude to me from being a small child has had a big impact on me.
She hated me almost as much as she hated my Mum, my dad moved away from me to be with her and her son (whose dad fucked off too) my Dad adopted her son, they had a child together but she was still extremely jealous. It was clear that she thought of my brother and I as inconvenient reminders that my Dad had been in love with and had had sex with someone else before her. My Dad never told her to get a grip and instead did everything to keep her happy, seeing us only a few hours a month, never spending any time alone with me, stopping maintanance as he had step brother and wife to support now, letting her punish me off for things like elbows on table, while her son was allowed to do it. The list is endless, and her son was a twat too as he was made to feel more important than Dad's actual children, (dad even removed my brother and I from his will when I was 8 years old to add step brother).
Even now, after Dad died and they have everything of his, photos, house, money etc but it's still not enough, they still text and call me and my mum names, I can't help that I was born first, and I can't change that my Dad loved my Mum first. Just as you can't change that your DP has loved his ex first, that he's had his dd first. Doesn't mean his second baby with you will be any less exciting for him as he's already done it with someone else. You need to accept that his dd is an equal part of his family, and that he is part of another "mummy and daddy" with his ex and if he's a decent Dad,masher will be around for years to come.