OK, I misread the details of your question. Your situation for 2018 is different because you all lived together.
For 2018, because the child lived with both parents more than half the year, either parent can claim the child as a dependent. If that is not you, you should delete the child completely (the turbotax interview does not handle this situation well). You don't qualify for head of household or to claim the dependent care expenses. The ability to "split" the benefits of a dependent only apply to parents who are divorced or separated or never married, and who live apart and share custody. Because you lived together, though unmarried, you can't split the benefits. Your husband can claim everything and you can't claim anything. You don't need to give your ex any forms.
If you paid the day care expenses and not your ex, your ex could claim the credit in his name. The idea is that the day care money was a gift from you to him and then he paid and claims the credit. But, if you each paid part of the expenses, then he probably is already maxed out on the amount he can claim and it won't make a difference.
Then, for all future years:
The only person who has the automatic right to claim a child as a dependent is the parent where the child lives more than half the nights of the year (183 or more nights). The IRS is federal law and is not bound by state court orders. There is no such thing as "equal custody", you have to actually count the number of nights if you aren't sure.
If the non-custodial parent is supposed to claim the child in a particular year, that requires that the custodial parent gives the non-custodial parent a form 8332 dependent release. This allows the non-custodial parent to claim the child tax credit only. The custodial parent always gets to use the child to qualify for EIC, head of household, and the dependent care benefit; these can never be waived, transferred or shared with the non-custodial parent. That's just federal law and it can't be superseded by a state court order or agreement.
The divorce order does NOT substitute for form 8332, unless the divorce order was signed in 2008 or earlier. In cases where both parents try to claim the same child, the IRS does not want to be in the business of reading court orders and trying to decide who gets to claim the child, if child support is current, etc. If the custodial parent won't sign the form, the non-custodial parent can go to family court and ask the family court to order the other parent to sign, but the non-custodial parent can't enforce the dependent claim through the IRS. The IRS requires form 8332, that makes it easy for them.
In turbotax, the non-custodial parent answers that they had custody less than half the year, there is a custody agreement, they do have a signed form 8332. This will properly claim the child tax credit only. The non-custodial parent will have to mail the form 8332 to the IRS after e-filing the rest of the return. If they don't send the form, the IRS will deny the child tax credit.
The custodial parent will answer they had custody more than half the year, there is a custody agreement, they will give the other parent form 8332. The program will properly claim EIC, head of household and the dependent care credit (if otherwise qualified) and will not claim the child tax credit.
If one of the parents gets an e-file block, then someone made a mistake.
<a rel="nofollow" target="_blank" href="
https://www.irs.gov/pub/irs-pdf/f8332.pdf">https://www.irs.gov/pub/irs-pdf/f8332.pdf</a>
So for 2018 taxes, no forms are needed because the child lived with your ex and therefore your ex can claim the child without extra forms. But starting with 2020, you will need to give your ex a form 8332 every other year. Or, you can give one form that specifies all the future years covered by the agreement.
