Clear boundaries and expectations help most teens (and, parents), I think.
While I understand that traversing teen years is a tug-of-war that, if done right, parents are supposed to lose at the exact moment a teen is able to claim responsibility, it needs to be scripted. A parent can't say it's OK to do "A" on Monday and have a 'cow' about it when the teen does "A" on Tuesday. As you recognized, your DH letting DD forego homework and not get enough sleep on a school night is a good example of setting fuzzy boundaries and expectations. Frankly, that kind-of stuff would be confusing and frustrating for anyone - add to that a hormonal teen and ... wow! It doesn't seem like something that would be a hard concept to get across to DH. Maybe it's time to have that discussion?
You want to avoid battles over the same "stuff" with DD. So, think about what you want from her on a day-to-day basis - chores, schedule, reporting, etc.. Make sure you and DH are on the same page. Then, sit down and discuss expectations with DD. Be brief (clear) and don't make it a negative talk. Allow for some discussion, listen and be prepared to make reasonable compromises. When you're done - write down the expectations on both sides - i.e., schoolnight bedtime is 9:30; no voices raised in anger; dirty laundry is to be placed in the hamper immediately; allowance is $ weekly and will be paid on Fridays.
When chores became a particularly "ugly" topic here, we moved it out of discussion. (The sound of my own voice repeating was annoying me and I remembered how, when I was a kid, I would deliberately NOT do something my father told me to do more than twice !) We got an erasable board where we wrote things like - "remember maritial arts class is at 6, so get homework done before dinner today" or "run the dishwasher and empty it when its done, please". That board saved our collective sanity. DD agreed to check the board every day and cross things off as they were done, and I agreed not to remind about anything on the board. We both made it work.
DH set aside time, every week, to do something fun with DD. For awhile, it was getting breakfast together on Friday mornings and, then, taking DD to school. Then, it was Sunday morning nature excursions. The point was 1-on-1 positive time, doing things they both enjoyed. They, of course, would talk during this time too and it helped create a stronger bond. DD is at college now, but she still looks forward to that 1-on-1 time wtih DH when she's home on breaks. She, affectionately, calls it "daddy-daughter time".
I would make the same effort to set-aside time to do positive, low-key things with DD. She often set the agenda. Sometimes it was shopping for "whatever" or "nothing". Sometimes it going for a walk. The point, again, was positive time.
Hope my experience has some application to your situation and that, in any event, you find peace.