Can I claim one child for child tax credit, but put both children down for EIC if I have full physical custody and their dad claims the other for child tax credit only?

My divorce decree has me claiming one child each year and their dad claiming the other. For the past 3 years, I've claimed 1 for a child tax credit but both for EIC. However, this year he is saying that is incorrect and I wasn't supposed to put both for EIC