I have read the full thread.
You absolutely have to take DD2. All your focus is on DD1 and not on her. You have one child with mental health problems so you have to do what you can to protect the other from them.
If Cahms say leave her with her dad then do that. give him all the info he needs and let HIM take on some of the responsibility. he ducks out of it because he knows you will always pick up the pieces for him and you need to stop enabling him and make him realise what an absolute shit storm yours and dd2's life is at the moment.
if he doesn't want DD1 then make him pay for private respite care. No options. he has to step up and sort this.
write down exactly what you want to say to DD1. its not that you don't trust her, you don't trust her "friend" the illness. and if she wont confront her friend and stop this then you will because you are at the end of your tether now. Tell her you are going, you have sorted out provision for her whilst you are gone and that's it. no further discussion. no pleading or begging or any other shit.
then go. keep in contact with her as you normally would but give yourself and DD2 some space.
You have to do this. because if you don't you are going to collapse with the stress of it all, either mentally or physically. then others will have to pick up the pieces and you wont be able to organise it to happen. so do it now whilst you can organise things.
whilst you are away, start drawing up the kind of contract others have suggested. you need to put her daily life on a really controlled footing as they would if she was in hospital. no ifs no buts no more shit.
why does she have 2 therapists? I am guessing this is down to DD1 again not liking one of them. if so, put a stop to this as well.
don't underestimate how miserable she is making life for DD2. you are only seeing whats on the surface not what she will be saying to her when you aren't there or not listening.
Having a mental illness does not give her a licence to behave like this.
I will be brutally honest, if you don't go on this holiday and make good on the conditions that you laid down, then you are in for a whole pile of it because her illness has won and it has proved to her that her friend is stronger and more dominant than you.
really for the good of your health your DD2's health and giving your DD1 a chance to improve, you have to go.
I hope that in reading what others with ED have said you draw some strength to take this step. I only wish you had the support that you need and deserve because honestly no one would want to be in your shoes. you must be one hell of a person to have coped for this long. you deserve that break.