Choosing between him or the dishes?

I know the subject sounds strange, but bear with me. This morning, for the millionth time, I awoke to a sink full of dirty dishes. Each night before bed, I clean the kitchen, load the dirty dishes in the washer, and set it to run overnight. Most nights, my husband, who is ADHD (diagnosed 2 years ago and taking meds but with no real difference in behavior), raids the kitchen and fills the sink with his dirty dishes (or leaves them lying around the house). I have asked (and begged) him hundreds of times to PLEASE put his dirty dishes in the dishwasher before going to bed. Small effort on his part, and makes my life so much easier. When I wake, I hit the ground running. Emails and phone calls from work to attend to, kids to tend to, dog to walk and feed, house to clean and manage. I need as much help from him as I can get, but instead he makes my life more difficult.

My husband and I both work full-time, but I feel like I do 99% of the household chores and childcare. I have asked him for help, and he usually agrees it but normally doesn't follow through (or will help for a day or two and then it's back to life on my own). 

This morning, when I mentioned to him that he once again forgot to load his dirty dishes, I got what I believe was his first honest answer: No. I can't. I'm incapable of it. If that's a problem for you, you must choose between me and the dishes.

The dishes, of course, are symbolic of the imbalance in our relationship and/or my inability to accept that he won't change. I can't live my life as a single mom if I am married to and living with the father of my children. I have this man who is physically present but mentally absent. He promises the world then delivers little. I feel like the only responsible adult in our household, and I have for a very long time. I feel totally alone, completely overwhelmed, and now very hopeless.

We have been together for 20 years. We have been in therapy for 2 years (but the therapist doesn't seem to want to focus on ADHD as an issue). We separated last year (he left me and immediately went on to have other relationships and basically abandoned me) though we are now living together again and trying to reconcile. He threatens to leave me often if I don't change. He likes high-risk behaviors and it scares me. I am doing the best that I can and don't know how to live like this anymore. It is so much more than the dishes: it is everywhere. I have been in individual therapy for 1 year because I simply cannot manage the stress of life with him. I also don't want to leave him: I love him and we have children together. He has not contributed financially in a while, and in fact has accumulated a lot of debt. He seems to struggle daily and has no real plan for his life (or has very unrealistic and risky plans). I worry about myself and our children.

He doesn't seem to think there is a problem, but when he does, he is convinced the problem is me. My standards are too high. The other day he told me that his problem is that I work too hard and do too much. I wish I had his problems! He doesn't see a need or possibility of him changing, and to the contrary thinks that he is fine the way he is.

I don't think I can accept that. I love him, but can't live with him. How am I contributing to the problem? Is there any hope for us? I am at the end of my rope.