We started overnights about two months ago. DS stays with XH every other weekend from thursday to sunday. We were still BF 5-7 times a day when this started and I was terrified! Luckily, he took milk fine in a bottle and we are working on the sippy. Supposedly he does fine with XH, although I don't feel like he's super truthful with me.
I do know that DS is super clingy like your DD for the first few days I'm home...Even after two months, although it is better now than it was at first. And I get clogged ducts every. single. time. It really sucks and I'm trying to wean very slowly to just morning and evening nursing.
Like pp, I would suggest trying to wean a bit, or at least getting her to sleep without nursing. Also, work on the sippy cup as much as you can till then. Good luck!