Snuggle I'm sorry this is so hard, this illness is shit in every single way. Please take comfort in the fact that where you are now is the hardest part of the journey and that recovery is definitely possible.
I would call your dds bluff, put rules in place about how much she needs to eat and if she decides to go and live with her dad that's a risk you'll have to take. My instinct is she knows that would be a disaster for her so she will threaten it but not actually do it (I obviously don't know your dd but I do know ED tactics they use to get parents to back off!!)
If you suspect purging tell your dd there's a no toilet rule for an hour after eating.
If your dd truly believes there's nothing wrong with her then she won't object to seeing a Dr then?! 😉 Use whatever leverage you can to get her to eat and don't be scared to put her in the car and drive to the Drs or a&e.
It sounds unlikely I know at this point but your dd wants your help, she is probably scared shitless and also really hungry!! She needs you to force her to eat as she hasn't got the strength at the moment.
Don't lose heart your dds in there I promise.