The custodial parent cannot allow the noncustodial parent anything when it comes to claiming any type of credit on a tax return. The Internal Revenue Code of the United States allows or disallows credits and deductions on a federal tax return.
The Internal Revenue Code of the United States cannot be overruled by a judge in a divorce proceeding.
From IRS Publication 501 Dependents, Standard Deduction, and Filing Information page 13 - https://www.irs.gov/pub/irs-pdf/p501.pdf#page=13
Children of divorced or separated parents
(or parents who live apart)
Example—earned income credit. Even if statements (1) through (4) are all true and the custodial parent signs Form 8332 or a substantially similar statement that he or she won’t claim the child as a dependent for 2018, this doesn’t allow the noncustodial parent to claim the child as a qualifying child for the earned income credit. The custodial parent or another taxpayer, if eligible, can claim the child for the earned income credit.
