I can well understand your feelings. It really is frustrating when trying so hard to be told 'you do not understand' or are 'not cutting enough slack'. Made all the worse because while at the back of your mind you think you are being taken advantage of there is always the fear that she is right, and very ill. A sort of paralyzing situation.
Your instincts seem to be going against what your daughter is telling you.
Just reading your post it seems as if your daughter is trying to control you - perhaps I'm reading too much into it - what do you think?
I'd suggest that whatever the case you need to have boundaries, basically for your sake to start with, but I suspect in the longer term for your daughter's good too. By boundaries I'd give as an example simply saying 'that's not on, I'm not going to be spoke to like that' and walking way without further comment when she treats you in an angry manner. If she fails to do something you were relying on her to do then say so and again walk away, don't argue or enter into a debate. If she accuses you of lack of understanding say nothing.
None of this is easy and in the short term may produce angry reactions in your daughter which will be hard to bear. I'd suspect the alternative, catering to her whims, would be worse as it escalated unchecked over time.
I'd think you very much need an ally in this situation, Do you have a partner or family member or friend you can discuss things with frankly on a regular basis? It is very easy to lose perspective and descend into feelings of guilt and loss of purpose.
Having a mental illness, depression, anxiety, BPD or similar is not easy, but neither is it an excuse to always treat loved ones harshly. When I've been very ill I've been standoffish, bad tempered, seemingly wrapped up in my self and other undesirable things. Even though the impatience and resentment I knew I was hurting others and as I improved I'd try to make up for it - I did care.
I would also suggest that you might benefit from counseling arranged though your GP. A professional opinion and support cannot hurt, you have a huge amount of stress on you. You care for and love your daughter and try so hard.
Please feel free to talk here as much as you would like, we do understand