Homely, I know it's really, really hard. I truly do. But there is a lot of evidence that children grow up happier and more successful on a range of markers if they have a positive relationship with both parents. It's hard and very sad that he and his family won't provide the sort of parenting kids ideally deserve, but it is, still, better by far that she knows where she comes from, and what her roots are, with that side of her family. Her father and his family do sound hard work and selfish, but they are also her family, and she needs to have a sense of them and her place in their lives to feel confident about who she is.
I suppose the answer is: you will manage a full weekend away from her because you love her, and good and regular contact with her father is what she needs, if she is to grow up a happy, stable person.
Second all the advice on trying to eat, and sleep, and be kind to yourself over the weeks and months ahead. It's very hard and stressful, I know. But in time, you may even find that the odd day to catch up with friends child-free, or even with housework, or some sleep, may be a positive. She's so very tiny still - as time goes on the intensity of the bond does start to lessen. Not the love, just the way they are almost part of you - the loosening of the apron strings slowly happens and they do get more and more independent.
Meanwhile, hang on in there and try to remember that she will be fine, and so will you. And this will be over, and a happy new life lies beyond this arrangement-making phase.