The confusion is the definition of the custodial parent and that lies at the heart of the situation. The IRS defines the custodial parent as the one with whom the child lives the most nights. Since the number of nights in the year is an odd number, both of you can’t be the custodial parent. That aside, since you and ex have agreed to 50-50 custody, the simplest solution is to agree that one of you is the custodial parent every other year. That custodial parent would give the other parent a signed form 8332 to allow that non-custodial parent to claim the dependency and child tax credit. But that non-custodial parent must file as single if unmarried. The custodial parent can file as head of household and claim child care credit and EIC even though that parent gave up the dependency. That may be confusing and counter intuitive but that is the tax law.
