That's correct, a child can only be used for one parent for EIC and not both. When the parents live together, only the parent that is claiming the child as a dependent can claim EIC.
That's not true when the parents live apart (as in a divorce situation). Different rules apply.
TurboTax thinks you don't live with the other parent and is awarding you the EIC. Delete the child. The only thing you can get from entering him/her is errors.
