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Only a custodial parent - with whom the child lived most part of the tax year - may claim a deduction for child care expenses.
Please let me know if you need any clarification.
If you have an agreement with another party and that party violated the agreement resulting damages for you - you always may sue that party for damages.
As from IRS prospective;
if non-custodial parents pays child care expenses - that is considered part of child support and may only a custodial parent may claim such deduction.
If you have unconditional agreement who will claim the child for dependency purposes in which year - and that agreement was approved by the court - it will be honored by the IRS.
If you have a private agreement - either signed or verbal - that is between you - and in case of disagreement s- either party may sue for damages and/or request for the agreement modification.