I totally hear you on the homework thing, and I cannot say as though I have all the answers.
My boys are a little older, so it is easier to get them to assume the responsibility for their own work.
But this is the way it used to always happen...
H would pick them up on a Friday night and they wouldn't even take their homework with. They would return Sunday night around 8, dig into their work and stay up however late it took them to get it done. Then the next day I would have tired crabby boys on my hands.
H didn't attend college, thinks that homework is dumb, school is boring and that homework is my domain. It cramps his style, and takes away his time as fun dad.
I wasn't getting anywhere with him, so I finally had to talk to the boys and suggest that homework not be left until Sunday night (ie it needs to go with them when they go with "fun dad"). S12 agreed, S15 said he didn't mind staying up late to do it on Sunday night.
They are both A/B students in honors classes.
I wish I had a good idea of how to address this with your D, I know how infuriating it can be to be the only responsible parent.
Count your blessings though that you are able to be that responsible parent. As I am now teaching in the schools I see so many kids who are suffering from dysfunctional family issues and/or uninvolved parents. It breaks my heart. And I do hate to generalize, but the kids from single parent families really do seem to have it worse off. I can sympathize though, as I now know how hard it is to keep it all together for us and them (the kids) both.
