Natalie, Sonja is right. This is a serious health situation for you and you must put yourself first. It's normal for kids to be zombies like this in their teens, I guess. But your kids are being very, very manipulative and it's not good. Can you take away privileges? I'm sure you've thought of that before, but sometimes you have to be really firm.
I had a friend once with a very unruly daughter. He explained to her that she had responsibilities and she was to live up to them or things would be taken away one by one. He did it and stuck with the punishment. In fact, one of the things taken away was the door to her bedroom so she had NO privacy anymore. Yep, he took it off the hinges and put it in the basement. That was the final blow. He made her earn each item back and eventually they got things back on track.
If nothing seems to work, then I think Sonja is on the right track. Let them go to school in rumpled clothes. Let dirty laundry sit until they do it. But, each time you give in, you set things back several steps. It's hard to make them believe you'll be firm when you feel guilty and give in.
I imagine they may be unhappy that you are in this situation and it seems like there is no way out. I know they would like a normal life with a mom who could go and do things with them at the drop of a hat. But sometimes life isn't fair. It's a tough lesson for kids sometimes. Since you are having problems right now with both of them, have you considered having some sessions with a counselor? Teens tend to be a bit self-centered and maybe an independent voice could get them out of that mindset.