Deductions & credits

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>
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**