You have 2 issues ... on the IRS side you are the custodial parent and have the superior right to claim the child however the divorce decree says the other parent gets to claim the dependent in 2020. If you do not allow this then you are fine with the feds but in contempt of a court order and can be in trouble for that if the other parent presses charges.
NOW ... because you are the custodial parent you still can claim the child for the HOH filing status and the EIC & child care credits. By waiving the right to the dependent exemption the other parent only gets the CTC. And the same goes for all the prior tax years ... there is no such thing as 50/50 custody in the IRS rules and since there are usually 365 days in a year the child cannot have possibly lived with both parents MORE than 1/2 the year unless you time it perfectly each year.
The IRS only recognizes physical custody (which parent the child lived with the greater part, but over half, of the tax year. That parent is the custodial parent; the other parent is the noncustodial parent.)
Who can claim the exemption and credits depends on who is the custodial parent. (By the IRS definition of custodial parent for tax purposes - this is not the same as the legal custody that a court might grant.).
The test that the IRS uses to determine the custodial parent is where the child lived for more than 1/2 (or greater part) of the year. The IRS will go so far as to require counting the nights spend in each household - that person is the custodial parent for tax purposes (if exactly equal and more than 183 days - The custodial parent is the parent with the highest AGI, if less than 183 days then neither parent has custody so the child cannot be claimed by either parent). And yes they are that picky.
See Custodial parent and noncustodial parent under the residency test in Pub 17
https://www.irs.gov/publications/p17#en_US_2017_publink1000170899
Only the Custodial parent can claim: (Child would be listed as non-dependent EIC & CC only)
-Head of Household
-Earned Income Credit
-Child Care Credit
The non custodial parent can only claim: (Child would be listed as dependent)
-The Exemption
-The Child Tax Credit
But only if specifically specified in a pre-2009 divorce decree, separation agreement or the custodial spouse releases the exemption with a signed 8332
