That is correct.
The following is a link to the EIC publication. It has all of the rules and a lot of examples, some similar to your situation, and discusses rules for children of divorced or separated parents on page 19:
The specific paragraph the summarizes what I have told you:
If a child is treated as the qualifying child of the noncustodial parent under the special rule just described for children of divorced or separated parents or parents who live apart, only the noncustodial parent can claim an exemption and the child tax credit for the child.
However, the custodial parent, if eligible, or another eligible taxpayer can claim the child
as a qualifying child for the EIC and other tax benefits listed on page 16. If the child is the
qualifying child of more than one person for these benefits, then the tiebreaker rules
determine which person can treat the child as a qualifying child.