I couldn't read this thread without adding a message a support for you Matilda.
I have no general adivice or grand plan as so many people seem to be influencing the relationship between you and your daughter, so it really is complex. I definitely agree that she is using you as a scapegoat and you are the focus of her frustrations because she trusts you to take it, and loves you.
I also think the inheritance could be a big demotivating factor for her to get help or recognise she has mental problems. The money will mean she can house herself and be independent no matter how she treats those around her and it will cushion her from many practical problems. How many 19 year olds can say that? It is too much power, too young IMO.
What happens if she is diagnosed as mentally ill? Could this ultimately affect her access to the inheritance? Is she afraid of this, or feel that you are pushing the therapy onto her as a way of preventing her from being able to access the inheritance?
What is she wanting to do after A levels? is she going to university or college or wanting to start work? Some of her friends will be leaving home now. Perhaps the best you can do is help her sort out a place at college or a job, find accommodation and then wave her off, just like lots of other parents are doing with their 19 year olds.
Whatever misgivings you have, I think perhaps now is the time to distance yourself and step back after you have seen her throught the exams.
Can you try to turn your conversations with her to practical sorting out for her future - where she will stay, what she will do. Stop going over old ground and saying sorry as it sounds like you cannnot say it more. When she is ranting to you about past mistakes, do all you can to divert the conversation to her future - practical, concrete, details like sending off forms, phoning the accommodation office, etc. If she totally refuses to seek therapy then leave it. She may change her mind only when she is in a different environment with different people.
What will she be like, I wonder, if you show her you are planning life around her - she going one way, you going another? seeig you concentrate on small amd more solvable plans of your own, rather than big, unsolvable issues of hers may change the dynamics of your relationship. Her behaviour IMO is forcing you to stop thinking about the future for either you or her, and that is a very bad thing. Don't let her do this.
If she is not looking for a course at college, than put your energies into getting her away from your home and doing something at least vaguely constructive with her life - staying with other family members or renting a flat and taking some training or gap year travelling. At least the inheritance means she can pay for travel and courses she is interested in.
How is your 16 year old son in all this? It sounds like your daugher may be grabbing all your attention for herself and the risk or your relationship with your son. If you and he are close this will keep you strong and reinforce the fact that you are a good parent. Don't ever let your daughter threaten this.
Must dash now, but hope something there helps.