OK, it sounds like someone needs to go over the complete rules package with you. This is all covered in IRS publication 501.
https://www.irs.gov/pub/irs-pdf/p501.pdf
I will answer your specific question but it will take a little while to get to it.
under federal tax law, in cases of children of divorced or separated parents who share custody, the only parent who is automatically entitled to claim all the tax benefits of a child is the parent where the child lives more than half the nights of the year. This is the custodial parent according to the tax law, and has nothing to do with your court custody order. It is entirely dependent on where the child lives the most number of nights. There is no such thing as 50/50 custody and you actually have to count the number of nights where the child lives in each home. (In most years, there are an odd number of days – 365 – so it is impossible for physical custody to be 50/50. One parent must be “more than half“. In a leap year like 2020, it is sometimes possible for custody to be exactly half the number of days. In this case, neither parent has custody “more than half the nights“ and this will become important later on.)
There can be an agreement for the non-custodial parent to claim the child as a dependent and get the $2000 child tax credit. In 2020, this may also result in a recovery rebate. However, the ability to claim the dependent care credit, earned income credit, and head of household status always stays with the parent who had custody more than half the nights of the year, and this tax benefit can’t be waived, transferred, or shared.
The way it is supposed to work is that the custodial parent gives the noncustodial parent a signed form 8332 dependent release. The custodial parent will indicate in their tax program that they had custody more than half the night of the year but they are giving the noncustodial parent form 8332. The custodial parent‘s tax program will not claim the child tax credit, but will make them eligible for the daycare credit, earned income credit, and head of household status. The noncustodial parent must enter on their tax return that the child live with them less than half the night of the year, but they are claiming the child because they received form 8332 from the custodial parent. The noncustodial parent’s tax program will give them the child tax credit but will not make them eligible for the daycare credit, EIC, or head of household status. The noncustodial parent must mail the original signed form 8332 to the IRS after e-filing, using a form 8453 cover letter, within three days of e-filing.
It is certainly possible to alternate custody and the dependent claim on the tax return by alternating where the child actually lives. But if you don’t actually adjust the child‘s living situation, and you have just been alternating claiming the child by lying about where they lived more than half the nights of the year, then you’ve been doing it wrong. The noncustodial parent may have been claiming excess benefits and the custodial parent may have been denied tax benefits by doing the procedure incorrectly.
Now to your specific question:
If you are not the parent where the child lived more than half the night of the year, you can’t claim daycare expenses. If you are the parent where the child lived more than half the nights of the year, you can claim the daycare expenses even though you don’t claim your child as a dependent. But you must follow the procedure above, by listing the child as living with you more than half the nights of the year and giving the noncustodial parent a signed form 8332. If the other parent has already filed a tax return by claiming that the child lived with them to get the full dependent benefits and not using form 8332, then when you file to claim the daycare benefit it will send up a red flag at the IRS and both parents will be investigated.
And finally, if the child lived in each parent’s home exactly half the year, which for 2020 would be 183 nights for each parent, then neither parent can claim the dependent care benefit or head of household status or EIC, because those are only allowed to the parent where the child lived more than half the nights, and exactly half is not more than half.
