You're a great guy, not a bad guy.
Heck, when my kids dad was on his meds and off the crack, and would actually be 'ok' enough to take them for a weekend or two even THEN he would be trying to get his 175/mnth to me lowered. 'well i had them three days this month, and uh 175 divided by 30 is x amount of dollars, so i'lll deduct x number of dollars for those three days this month' --- if you have custody, then she should be paying You, not the other way around and I am quite sure the child support/alimony would at least cancel each other out.
You aren't greedy and that's great, but then maybe give the money you give to her to a children's or city charity or something Would probably go to better use or better yet, use it for a new Playstation for the boys