Hi
IngridD 
I'm sorry and you are right, it is just so tough when you are in it and severe anorexia, BPD is. I'm glad your daughter is making progress, she managed to overcome a severe eating disorder is a huge step forward.
Has your daughter shared her reason wanting to be transferred to a new unit? Is it in the same hospital? Supporting the family is paramount and that includes facilitating contact and de institutionalising. What's your medics view, advice been on your daughter not wanting to see you, and the recent request for transfer?
That you still feel close to her after you've both been, going through says all to me, keep the door open as you say. When my 30DD came out of crisis (she lives at home) she said she felt gratitude and kindness she was unable to feel when she was so very unwell, fearful and in pain.
Do you have support at home, family, friends?
WDx