Deductions & credits

It sounds like he doesn't agree any more.

Only the custodial parent can claim HOH and the child care credit.  Using an FSA follows the same rules as the child care credit.

In your situation the first tie breaker is total # of days.  Where did the children live the final month?  For example, if they lived with him weekends in December, they might have lived 340 days with your ex but 350 days with you. That makes you the custodial parent.  

(If the # of days is exactly equal, the second tie breaker goes to the parent with the higher gross income.)

See here under "special rule for children of divorced or separated parents."  <a rel="nofollow" target="_blank" href="https://www.irs.gov/forms-pubs/about-publication-501">https://www.irs.gov/forms-pubs/about-publicati...>