The IRS goes by physical custody, not legal custody.
It is allowed for you to arrange the children's schedules so that the child spends more than half the year with the father one year and more than half with the mother the next year so that you are each the custodial parent in the year you claim the child, so that you can claim full benefits.
In order to claim EIC, you only need one thing: for the other parent to agree to "let you be the custodial parent" for 2018. That means he cannot claim the EIC, dependent care credit or Head of Household, based on that child.
