Don't know how this is going to go but we have been on edge of throwing her out before for stunts like this. Is this what we have to do to save DH from total breakdown. When she decides she is doing something there is no compromise, no care of the impact on others. It seems the more understanding and caring we are the more she takes. Someone please give me a plan to change this before she throws away a lovely home and family.
You need to acknowledge that there is no way of looking at this statement other than as a firm belief that it is DD's responsibility to prevent her dad from a total breakdown and that DD owes you and her father this. This belief is toxic and it has to be banished.
You are very quick to grasp at suggestions that DD needs a diagnosis and to be fixed. However, I suggest that both because DD would refuse to engage with any talk of fixing her and because this is a family problem, you and DH need to start with yourselves instead, if you are interested in changing things and not just manning the barricades until DD leaves home.
You should start with yourself. It is not your job to protect DH or maintain his equilibrium or to make others do so. You have to stop trying to do that, and establish proper boundaries between you and him. This means understanding that his emotional reactions are his own and that you owe him no supporting response. It means you expecting him to seek help from his MH professional and not expecting his family to adjust, accommodate, work around.
It is not DD's job to protect DH either but you will see that once you have done some work on your own sense of boundaries and have created a few between you and DH. Hopefully once that happens you will see that DD is not you, and did not sign up for whatever you understood your relationship with her father to be, but has her own road to travel though all of this and is owed support in negotiating it by both parents. Other posters have suggested this but I don't think you are receptive to their suggestions.
DD is looking for something from you and her father that she is not getting. You need to stop the heart to heart talks, and any picking over of DD's feelings that you hope to accomplish in your sessions needs to end.
Those conversations are not emotional support. They are putting DD under a microscope and pathologising her. Nor is giving her things on demand supportive in any way.
Emotional support involves giving her a framework where she can anticipate what will be happening in the family -- family scheduling meetings that were mentioned by a PP would be ideal. That way she would know if she was expected to be in a certain place at a certain time and could plan accordingly. Or if you are going to be away from home, you could all agree to check in with each other by phone or facetime at a given time just so that you can say goodnight, make sure she has set her alarm for the morning so she can get to school, etc.
Emotional support means not being afraid of saying no when no is what you mean -- it is much easier to do this within an already agreed framework/calendar, or within an already agreed budget (DD needs to be paying for herself at this stage of her life). So I really strongly suggest you start getting yourselves organised and improving straightforward communication, using the calendar as a useful and neutral tool, with everybody's input welcomed and attempts made by all to understand relative importance of dates/times.
I suspect DD would see that she could fit in more studying/homework if she were to get a good visual handle on each week in advance. However, in a teen's life things can crop up and there should be an element of flexibility on your part if work has been done and grades improve.
Emotional support is the opposite of using guilt to get things done your way or getting others to support your unhealthy agenda. You say you have shielded DD from any suspicion that she caused DH's MH problems, but you also state several times here that you felt she owed you something, and I suspect you use guilt to manipulate her more than you perhaps realise:
We say yes more than 9 times out of 10 and ask her to consider us one night
and
We were asking, for once for her to put us first. For the first time in months. We have done lots of things for her, talked us into buying various things. We've dropped our plans for her convenience, rarely do we ask her to do anything like this and for one night, so we can have a stress free night, not worrying about her or having our evening disrupted by visitors and giving lifts. Just once. She can see boyfriend any day this week. I have given her lifts to his and him lifts home. So just once can she not put her plans on hold for us.
I wonder how much of that exasperation you conveyed to her?
Emotional support means being explicit in your assumptions and your expectations, not keeping a mental ledger with debit and credit columns and DD coming up short every time. You seem to have the clear expectation that favours on your part are given in hopes of receiving a quid pro quo. Your anger here was partly due to a feeling that you are owed consideration and have been owed for the last four years, and a feeling that DD has failed to meet your expectations. You cannot expect DD to read your mind or to understand things that you have not been explicit about. If this is how you feel then you need to communicate that to her. But first, ask yourself if it is a realistic expectation on your part when someone has, for instance, no car.
Emotional support also means real consequences for breaking doors or other damage. So you need to consider warning her that you will call the police next time, and you should not treat material damage as a personal insult or yet another nail in the coffin of DH's equilibrium. Emotional support involves showing DD exactly how far she can go in real life and not in terms of DH's fragile state and your lack of boundaries where he is concerned. You are teaching her nothing useful if all she understands of consequences comes from life within your four walls as it is right now.
Emotional support means showing her how to fight fair, how to negotiate, how to compromise. She has not learned this so far because DH is so fragile and because you are secretly trying to store up her goodwill in order to cash it in. So DH must deal with his problems and you must learn how to set your own boundaries, stop manipulating and plamasing (an Irish word for a less than open and honest style of communicating; disingenuousness, having a hidden agenda), and start parenting DD and partnering DH in an adult way.