The custodial parent has first priority on claiming the children on her taxes; regardless of the amount of support provided by the non-custodial parent. The IRS goes by physical custody, not legal custody. 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.
Even if you have your own agreement on claiming them, the non-custodial parent must still get form 8332 from the custodial parent.
For tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent. The IRS goes by physical custody, not legal custody.
Yes, the IRS expects you to count the numbers of nights the child sleeps at each parent's home. It is allowed for you to arrange the children's schedules so that one child spends more than half the year with the father while the other spends more than half with the mother. Then you are each the custodial parent of one child.
It is allowed for you to arrange the children's schedules so that the child spends more than half the year with the father one year and more than half with the mother the next year so that you are each the custodial parent in the year you claim the child, so that you can claim full benefits.
