It sounds like you are trying to use the circumstances used for never married or divorced parents who share custody of a child. In that situation if there is a signed Form 8332, the custodial parent can file as Head of Household, get earned income credit and childcare credit, while the non-custodial parent gets the child tax credit. The IRS cares about physical custody. The custodial parent is the one with whom the child spent the most nights--at least 183 nights.
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