Understand that the IRS pays no attention to divorce agreements but has its own rules. The primary rule is that the custodial parent- -the one with whom the child spends the most nights- -gets to claim the child with all of the tax benefits. In your case you both would agree that one child spent more nights with one parent and the other child with the other parent. In that case each of you claims one child and is entitled to the child tax credit, earned income credit, childcare credit and can file as Head of Household if otherwise qualified. Now if the children truly spend the majority of time with one parent, that parent only is the custodial parent. In that case the custodial parent can give the other parent form 8332 so the non custodial parent can claim that child. The non custodial parent can then claim child tax credit but the benefit of the earned income credit, child care credit and right to file Head of Household if otherwise qualified stays with the custodial parent even though the other parent claims the dependency.
Let us know if any of this is unclear.
