Sounds like the ex-wife in this case needs to put on her big girl panties and ddeal with her issues, not the least of which is that she is still terribly bitter over the divorce and now seems to live to make this guy's life miserable. Truthfully, if she was my friend and she asked my opinion, I'd tell I thought she was pathetic.
Divorce is hard...no two ways about it. But I would really try my best not to make it worse by being a nasty, vindictive witch. She has a decent ex-husband who sounds like he is trying to do the best he can for their child, and she's going to go after him for a small amount of $$ that he may earn from some part-time job.
I think that if she does end up doing that, then he'll have to tell her that all the "extras" will have to stop. She'll get the child support payments and nothing else...no new clothes, no school supplies and so forth. She will be required to provide for all of that stuff out of the support payment.
I know a couple who divorced and their child literally has 2 complete sets of clothing, toys etc...one at each house...because of a situation like this. The Dad was providing child support plus extras. The Mom would send the kid for the visitation in the rattiest clothes imaginable so that Dad and stepmom would have to buy her decent clothing. Meanwhile, the kid had decent clothing at Mom's house...Mom just didn't let her bring it to Dad's, so that Dad would have to spend more $$$. For a while, Dad would let kid take new clothes back to Mom's, but it got to be that every time they got kid for visitation, they'd have to buy her clothes...Mom never sent her with the new clothes purchased the last time...just kept sending her in the same ratty stuff. Finally, Dad and stepmom decided that the stuff they bought kid would stay at their house when she left after visitation, so it would be there for her to change into the next time she came dressed in the ratty clothes that Mom always sent her in. It was sad in a way, but I could see their point in a way too.
I find women who have no desire to take care of themselves pathetic. I find women who continually play the "poor me" card to be pathetic. It's a bad example to set for your children. It's a pathetic, sad way to live your life.