My daughter is a little older than yours, but she has had depression, anxiety, panic attacks and multiple medical issues for a long, long time. And she seemed to consistently be argumentative and often combative, and unwilling to concede an issue or even to see the other person's point if it's different than hers (where no one is wrong, just a matter of preference).
It seemed like we couldn't even have a discussion or remind her about a chore around the house without her ending up panicking or sobbing or sometimes even threatening to harm herself.
Regular parenting wasn't working (we have a son who's a few years older than our daughter and I guess you'd say that traditional parenting worked fine with him; he's healthy and happy and responded well to logical consequences, he did his chores, did well in school, etc). We tried all kinds of ways to reach out to our daughter, all ending in failure, fights, tears.
Anyway, what helped was going to the counselor together. We contacted the counselor (her dad and I) and left a message saying that we needed help communicating, without our daughter ending up screaming or crying or flying into a rage. The counselor set up a meeting for all of us, where we were all able to express our thoughts with the counselor as a referee, guide, and coach. She helped us stick to the subject. We said things like "we want to be able to say/ask/remind this or that without [daughter] immediately saying we don't understand or she's too depressed or whatever". [Daughter] replied by saying that when we ask/say whatever, she feels whatever. Saying it aloud helped tremendously. At one point the counselor said to our daughter "do you hear what you're saying?" and our daughter had to say "yeah, that makes no sense now that you're making me aware of it". The counselor also helped her dad and me to understand how depression and anxiety makes a person feel, and how not to make excuses but how to approach things differently, and how to effectively parent a kid with mental illness. We worked on specific things that were consistently difficult (how to get her to help around the house, for example) and on general things. The counselor was really good at helping us stick to the subject. We met I think two or three times and then regular counseling sessions resumed with just our daughter and the counselor.
So, that's what helped us. It's never going to be all rainbows and kittens, but it's much better. Maybe something similar would help you. Make sure to keep the subject about how to communicate with your daughter, not about how it makes you feel, because the counselor will still be your daughter's doctor, not yours. Our counselor made that clear. For example, she set up guidelines. She said things like "if you as parents are fighting or arguing over this, we won't address that here. If it's making you feel inadequate or like failures as parents, we won't address that. That would be a separate issue. This is specifically about my patient (our daughter) and how to help her communicate more effectively and calmly with her family".
There's also an organization called NAMI (National Alliance on Mental Illness) that has support meetings for caregivers/parents/family. You can look them up and see if there's one in your area. Or maybe contact them for support or help.