It's sort of a tough call...often if he's paying child support, that's the "support" they consider. Is he not paying the full amount? That would likely look bad. Has he already filed? If he has, you're out of luck, filing and claiming the kids would cause problems because they'd show up twice. Did you fill out the form to authorize him to file? (I don't remember the number, 8???, but he might be able to without if there's a court order.) So is there a court order, as in, did the courts sign off on your mediated agreement, or is it just part of the package that's still in the system and not final? If it's not final, and he hasn't filed, and he isn't paying his full child support or providing the other things, then I'd go ahead and do it.
(Sadly, though, actual physical custody has nothing to do with it anymore...just one more way women w/kids are squashed under The Man. My ex, for instance, was awarded BY THE COURTS both kids, even though he sees them a few weeks a year. The thing they looked at was our income, and since he was making a whopping 16,000 a year to my part time job that I'd just started, he got both. But he's been good and actually let me claim them w/o a fight this year... Crazy when your ex is more decent than the courts...)
(Sadly, though, actual physical custody has nothing to do with it anymore...just one more way women w/kids are squashed under The Man. My ex, for instance, was awarded BY THE COURTS both kids, even though he sees them a few weeks a year. The thing they looked at was our income, and since he was making a whopping 16,000 a year to my part time job that I'd just started, he got both. But he's been good and actually let me claim them w/o a fight this year... Crazy when your ex is more decent than the courts...)