Hey Jezzy, hang in there!
Try to remember that nothing she does is personal to anyone except herself! She is still (and for years yet to come) operating from a level of total narcissism that is completely appropriate for little ones. So when she pushes you away for Daddy, she is not pushing YOU away, she is pushing HERSELF toward him. When my son does this I try to remember that he's not pushing ME away, he's pushing away a kind of love and security that he doesn't need in that moment. Then I try to get happy about his desire for independence, and the free time it may bring me.
At the same time, you have an opportunity to teach her that no matter how much she wants something, it's not ok to hit anyone. And you can keep parenting her while she's running away by modeling some good language for her, like "I really really really want my daddy right now! Please help me get daddy's attention!" or "Let me go, I need to see my daddy, please let me get down so I can run to him!" or "I'm so frustrated because I want my daddy to be here and he's not here and I miss him!"
I'd be so resentful in your shoes about the inequality of childcare in your relationship, but I understand that some relationships make things equal in other ways. Your child is moving on to the phase of childhood where she creates other relationships, and you had a super sweet time while you were her only relationship. And here she goes, investing in the one person who could have been right there with you but wasn't. I hear that this is the challenging thing right now for you. My suggestion is that you not let her definition of "go away mommy" be the only way to do it. You can and must keep parenting her even while she's moving out into the world (and in your house, that's daddy.)
Try to remember that the physical and emotional care you've been taking of her was in service to her as an independent person, not for the purpose of making her love you most. Ultimately it will mean that she'll be able to trust you most when she really needs you, but it's your support of her as a whole being separate from you that will fill her with love.
If I had a daughter, I'd try to also remember that her screaming pushing tantruming demand for daddy time is something I'll want her to have in all future relationships - the sense of absolute entitlement to that love and connection, and the strength to fight for it when she wants it. This is exactly the time when her awareness of gender and her sense of power as a girl is getting expressed and she needs to sort that out with her main man, daddy for now.
You haven't said if he's responsive to her needs or not, and that would be another way you can support her. You could coach him in responding to her with enthusiasm, love, without losing the limit setting that she needs from all her parents. eg "Honey! I'm so excited to see you! I can't wait to hug you, but I don't want you to hit anyone - please give mommy gentle touches in the future. Ok? Now come here and lets snuggle!" (And if he's not coachable, or not really responsive to her, then you have to parent her through that - the same way you might have needed support with an unresponsive boyfriend. She'll need help keeping her self confidence high even if he's not accepting of her.)
Your special mama skills are needed now just like they were for that tiny helpless infant she was. But the snuggly reward that you long for... it has to be on her terms. And I'm saying that as someone whose mother has been deeply loving all along, but could never see me for who I am because she so badly wanted me to be a particular kind of little girl (just like her). I yam what I yam, and I've missed having a mother who could see that and love that, as much as I feel her love in a general way.
Mom of one child (2008), wife of one husband, tender of dogs, cats and chickens. Household interests: ocean life (kid), bitcoins (husband), simplifying (me).