If it drifts into her pressuring me into trying to get stuff off me though and I can't talk her round from it and back onto feelings then what would you do? Just sit there and continually say no you can't have .. Because... I do care about you but you can't have... I do want you to have a nice life but that doesn't mean I have to agree to... Honestly. Would you sit there for hours doing that?
Use the phrase 'I'm sorry you feel that way, DD.' And repeat. You don't have to go at it like a bull at a gate. If you can't talk her around why try for so many years? This is an example of you needing to change your tack. It is also an example of you seeing the glass half empty, being caught up in a pattern involving unhealthy communication habits, being enmeshed, and catastrophising,
All of you are locked into an unhealthy pattern of communication where everyone wants to 'win'. The only reason everyone wants to 'win', and tries to 'win' every encounter, is that everyone believes they can 'win'. This investment in 'winning' is also why you keep on taking the same approach to DD and why you are averse to suggestions that you need to change your approach, reframe events, examine your lack of boundaries, as opposed to your welcome of suggestions that DD has something going awry that needs a diagnosis. As a PP has said, a diagnosis will only mean you even more urgently accepting the need to change how you deal with her and with DH. But I suspect a diagnosis would affirm your belief that you are 'right' and were right all along, and the problem was DD.
Winning in relationships is not possible. None of you is behaving in a mature way. You need to sit down and examine what 'winning' means to you. You need to ask yourself if DH has an agenda that involves him 'winning' too and you need to be brutally honest with yourself about this. This investment in winning is an offshoot of catastrophising -- none of you can see a middle road between win and lose, triumph and harmony vs. annihilation and destruction of the family by a rampaging DD, who destroys relationships, throws away her chance at a happy family life, etc.
Blytheandsebastian and Mulranna used the term 'catastrophising' upthread. DH does it. You do it too. The catastrophising is a huge issue and you need to address it. You can prevent yourself from falling into the catastrophising trap by building healthy boundaries between you and DH where you accept that he is the only one responsible for maintaining his own equilibrium. When you do that you will immediately remove from the equation your concern that DD exacerbates DH's condition. You will find the unhealthy triangular relationship that currently exists will be disrupted once you have healthy boundaries in place between you and DH. The key to solving this lies in your control -- it will be to establish healthy boundaries between you and DH.
DD has learned to catastrophise and to seek to win at all costs most likely from you, but all teens catastrophise to some extent. Everything is of the ultimate importance and they tend to be self absorbed and inconsiderate, even the best of them. They learn not to do it partly by just going through the process of neurological development but partly by the example of their parents, so you must stop it. But seeking to win at all costs is something she has picked up in a home where she understands the only alternatives are win or lose.
Almost every post of yours here reveals your mental habit of catastrophising.
This as well as enmeshment is what you need to examine when you go to family therapy, which you need to do even if DD won't go.