Can I claim my child as a dependent for the EIC and his father still get the childcare credit?

[DoninGA]

No.  If you are the custodial parent then the non-custodial parent cannot get any type of credit or deduction for the child unless you relinquish your claim for the child's exemption to the other parent with a signed Form 8332.  And even then the other parent cannot get the childcare credit.

[Hal_Al]

No.

 There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.

Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the exemption to him.

If you and the other parent live together, only one of you can claim the child for any tax benefit. The TurboTax interview is confusing (it's designed for divorced parents). The second parent should not enter the child, at all. 

[Hal_Al]

If you and the other parent live together, either one of you (but not both) may claim the child. You may decide between you which one will claim the child. Only if you can’t agree, do the IRS tie breaker rules apply, to see who has first choice. It may be worthwhile to prepare trial returns, both ways,  to see which way the family comes out best. This tool may be useful: <a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1">https://turbotax.intuit.com/tax-to...>.

[macuser_22]

Right.  Two possible issues here:

1)
If you both live with the child, you can agree who claims the child and all the benefits.   The child can only be on one return and not on the other at all.  The benefits cannot be split.

Per the IRS: in order for parents to split the benefits the parents must have lived apart at all times during the last 6 months of the year, whether or not they are or were married.
<a rel="nofollow" target="_blank" href="https://www.irs.gov/publications/p17#en_US_2017_publink1000170897">https://www.irs.gov/publications/...>

The dependent interview is confusing since it asks about custody without really explaining what that means.   That can lead you to answer the questions in a manner that gives credits to both parents when they both live with the child which is not allowed.   The child can only be on one parents tax return and not on the other at all.

*Only* divorced or separated parents that have lived apart for the last 6 months of the year can have a *custody* agreement.   The parent that physically lived with the child is the custodial parent and the parent that did not live with the child the non-custodial parent.   Under those circumstances the custodial parent can release the child's exempt to the non-custodial parent who did not live with the child with a 8332 form (which is a custody agreement).  

When *both* parents live with the child, no such custody agreement can exist since both parents have equal custody and there is no non-custodial parent.   The dependent and all the benefits can only be claimed by one parent.

And 2)

Only the parent that lived with the child more than half the year (custodial parent) can claim the child care credit.

Child care is "work related".  It can only be claimed if the care was necessary so that you (and your spouse if married) could work.  Only if the child lived with you more than half the year *and* the care was required so that you could work is it allowed.  If you did not live with the child or work at the time that the care was provided then it was not necessary so that you could work and therefore is not allowed.

See IRS Pub 17 page 213
<a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p17.pdf">https://www.irs.gov/pub/irs-pdf/p17.pdf</a>