Can she allow her father to claim my child?
How do tie breaker rules come into play here?
Am I going to have to be the one to pay back the IRS?
Can she allow her father to claim my child? Yes he can if the child lived with him as a qualified dependent, he doesn't need her permission if she doesn't file a return. In fact he probably claimed her as well.
How do tie breaker rules come into play here? Since you have no right to claim the child there is no tie to be broken.
Am I going to have to be the one to pay back the IRS? Yes you are. In the program, if you had answered the dependency questions truthfully then the program would not have allowed you to claim the child so you are responsible for the data input error.
The custodial parent has first priority on claiming the children on his/her taxes; regardless of the amount of support provided by the non-custodial parent. The non-custodial parent can only claim the child as a dependent if the custodial parent gives permission (on form 8332) or if it's spelled out in a pre 2009 divorce decree. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time, regardless of what any legal agreement says.
There is a way to split the tax benefits. For future negotiations with the other parent (and maybe even for this year) the following info may be of use:
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the exemption to him.
*If the child lived with each parent for an equal number of nights during the year, the custodial parent is the parent with the higher adjusted gross income (AGI) (2012 Pub 17 pg 28).
If you do not meet the custody test, then the only way that you could claim the child's exemption would be if the custodial parent gave you a signed 8332 form for you to attach to your tax return.
Absent a court ordered agreement granting you the tax credits, the 8332 is totally voluntary for the custodial parent. If there is such a court ordered agreement, and the custodial parent refused to issue the required 8332 form, then your relief would be through the court that issued the order to enforce it and compel the custodial parent to provide the form. The IRS will not get involved in disputes, that is up to local courts to resolve.