You are right that under federal tax guidelines, the entitlement to claim a child as a dependent for tax purposes primarily relies on satisfying the criteria for the child tax credit. This includes stipulations that the child must live with the claiming parent for over half the year and that the parent must provide more than half of the child's financial support. These stipulations seem to disqualify your ex-partner based on your description of the circumstances, notably the limited physical custody and financial contribution.
However, it's important to note that divorce decrees or separation agreements can designate tax benefits differently from the IRS's default rules. Specifically, if such an agreement grants the non-custodial parent the right to claim the child as a dependent and this is formalized with the custodial parent's completion of IRS Form 8332, this arrangement takes precedence over standard IRS regulations.
It sounds like that may have happened here. You can learn more about how the IRS handles dependents for divorced parents here.
In scenarios where the non-custodial parent doesn't meet the IRS's criteria due to significant changes in custody or financial support, and there's a prior agreement permitting them to claim the dependency exemption, you might need to explore modifying this arrangement. Modifications can be pursued if there's been a substantial change in circumstances, warranting a reevaluation of the original terms. This often requires legal consultation to understand the best approach to renegotiate these terms or to seek a court's intervention for amendment.
For more information, read our article "Claiming Your Children on Taxes After Divorce." If you would like to speak to one of our divorce attorneys about your options to modify your separation agreement please contact us at (303) 688-0944 or go here for more contact options.