You will have to print and mail in your return. Include a letter of explanation outlining why you should be able to claim the child as a dependent. The IRS will review the situation and decide who is able to claim the child for the purposes of head-of-household status, and credits.
One of the tie-breaker rules the IRS uses is:
If the parents don't file a joint return together but both parents claim the child as a qualifying child, the IRS will treat the child as the qualifying child of the parent with whom the child lived for the longer period of time during the year. If the child lived with each parent for the same amount of time, the IRS will treat the child as the qualifying child of the parent who had the higher adjusted gross income (AGI) for the year. [IRS Pub. 501, p. 16]
For more information, please see IRS Pub. 501 - Dependents, Standard Deduction, and Filing Information
