Before I put in my advice, I would like to state again that I have worked in tax prep for 14 years. --
(Tax preparer--NOT to be confused with CPA or tax attorney.)
1) There is no legitimate filing status called "single head of household" ( a common misconception based on the fact that most people filing head of household are, in fact, single)--
Right! My stated "single" wasn't referring to marital status, but was meant to designate the sole (single) person supporting the household. It's okay if you're married as long as you didn't live w/your spouse for any portion of the tax year. The one category that excludes using head of household is married filing separately.
2) As MSM stated previously, it is not at all uncommon for divorced couples to have the "every other year" arrangement. If a child is born to two parents, why should only one parent benefit from the dependency exemption?-- They should definitely have the opportunity to use the exemption equally IF they provide equal support. Say for instance, Dad pays zero support during a given year and claims the exemption, which reduces his tax liability considerably. He could theoretically make money by using a child for whom he paid NO support, while Mom, who received no assistance in supporting the same child, actually loses money because she cannot claim the child she supported. Any decree/modification allowing a NCP to claim a child as an exemption should include a statement that this is ONLY allowed if all child support and other stipulated expenses to be paid by that NCP are current at the end of the year.
3) If the child resides with you for more than 6 months of the year, then even IF he wins the exemption every other year, you will still retain the right to claim head of household filing status, and you will still be able to collect Earned Income Credit if you are eligible.
Having worked in the tax field for so long, my advice (to cover yourself with the IRS) would be:
IF he wins and gets to claim your child every other year, have it written into the modification that it is not to affect your ability to file head of household nor your ability to claim Earned Income Credit (if you qualify)