Her mother and you each qualify to claim the child. The tax laws say that if the parents can't agree on who will claim the child, then it's the one with the higher AGI. So if you claim her, you get HOH filing status but her mother can do a policy allocation that would require you to file form 8962 and report the allocation.
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For purposes of the PTC, your tax family consists of the following individuals.
1) You, if you file a tax return for the year and you can’t be claimed as a dependent on someone else’s 2025 tax return.
2) Your dependents whom you claim on your 2025 tax return.
Your family size equals the number of qualifying individuals in your tax family (including yourself).
This is a link to Form 8962 instructions. Allocation Situation 4, starting on page 19, covers the situation where a policy is shared between two families (the other 3 situations don't apply).
https://www.irs.gov/pub/irs-pdf/i8962.pdf
This covers the situations where you agree to an allocation or when you can't agree
I would suggest neither file their return until the policy allocation is settled because the allocation, which can range from 0% to 100%, can significantly affect your tax liability. That is the total tax liability for each of you and for both of you in total can vary based on the allocation.
