Quick answer
A family agreement and federal tax eligibility rules are not the same thing.
Do now
Gather the parenting schedule, support agreement, prior tax returns, and proposed tax provisions. Ask a tax professional which benefits apply and whether a required release or form is needed. Coordinate timing to avoid conflicting filings.
Watch for
A court’s allocation of a tax benefit may require additional federal paperwork; not every child-related tax benefit follows the same rule. Do not rely on an old tax-year threshold or an informal promise.
Official sources
IRS — Dependents: State Court Orders and Federal Tax Rules, NY Courts — Divorce frequently asked questions, DC Courts — Divorce.