My former sister-in-law ran into a similar situation: when she sent the kids to their dad's, they'd come back missing most of their clothing, their school shoes, a backpack, etc.
She went to Goodwill and bought clean, serviceable clothing and shoes, which she handed to her ex in a suitcase the next time he picked the kids up. She sent no school clothing, no good shoes, no special backpacks or library books.
Most importantly, she told the kids that the suitcase contained enough clothes for dad's house, and she didn't get into it any further. She didn't tell them that their dad was irresponsible, and she didn't say things like "your lazy dad can't even bother to find your shoes". They were young, but not toddlers, and they were old enough to understand that they were to leave the suitcase clothes at dad's.
I think it's important for your daughter to get some things put into place with the court, such as child support being paid regularly. As the kids get older, there will be more expenses (braces, school trips, etc) and it seems like things between the parents need to be more organized, legally speaking.
She'll need to learn to say no. Perhaps a counselor or adviser or priest or minister can help her find the words to say to her ex when he demands things and tries to manipulate and control her. She'll need to be able to speak up, to say "no". She can even have a memorized script of sorts, like "I won't do that, and that is your responsibility". If the ex is asking for things for the kids, like field trip money, or money for clothes, she needs to tell him that she will take care of that on her time.
She should care about the support. Even if she doesn't need money, the kids will down the road. She should put any leftover money in savings accounts for later (college, 1st apartment, etc). It's not about money, it's about the father's responsibility. By showing him that she doesn't care about the support and is ok with his paying support when he feels like it, she's showing him that she doesn't really care about how she and the kids are treated. If she gets firm on the support with the courts or a lawyer, she'll show him she can't be pushed around.