Why don't you spend your energy figuring out a parenting plan that gives them equal time with both you and your ex and makes it a set routine? Equal parenting time is best for kids.
There is lots of evidence that shows women get bigger support payouts when they keep the kiddos. While it wasn't the main reason I argued and won primary custody, it was in the back of my mind. But obviously, you never want to admit that to the judge. Research the support formulas for states in your area. More of his money in your pocket is of course better for the kids, right?