You do have the OPTION to let him fully claim one or both children. Because of the FSA and because you both have similar incomes, it would probably result in the best OVERALL refund (between the two of you) if you allowed him to fully claim one of the children.
Besides the Child Care Credit (usually $600 per child), you would lose the exemption (usually $600-$1000, plus State) and the Child Tax Credit (usually $1000). He would then gain those, but his Child Care Credit/FSA would be likely be higher than $600.
You could 'test it out' and start to amend to see how much you would lose. You could then ask for that amount from the other parent.
On the other hand, it may be more work than it is worth. Also, I wouldn't recommend starting to amend your Online tax return unless you were actually going to amend (with the CD/downloaded version, you can 'Save As' a new file, so you keep your original file, but the Online version would overwrite your original information).
