B.M.
I don't know NY law, but in Oklahoma (where my custody agreement is) they have what is called "right of 1st refusal". It basically means that when the parent who is not in "possession" needs to find childcare (aside from what is regular for the kid) they must allow the "parent-not-in-possession" the opportunity to ADD to their schedule.
So, on the weekends that are not your weekend, you would have the option of TAKING them extra - not switching out. It won't reduce your child support. However, after you have established a period of increased visitation, you can modify your decree so that you have your boys extra time.
You can't make anyone else behave the way you want them to (or even the way they should). BUT, you can try to spend more time with your boys - that seems like a win-win.
I know you know this.....DON'T bad-mouth your ex to the kids.
Good Luck!
Good luck!