Can I claim my child for EIC if my ex claims as a dependant?

I am trying to get some clarification. When I divorced, it was put in the paperwork that my ex will claim our daughter as a dependent and I will claim my son. We have joint custody we get the kids week on/week off so it is basically equal all year. She makes way over the limit to qualify for EIC regardless of how many kids she claims so doesn't claim EIC at all. I do qualify for EIC, so I am trying to figure out if I can claim both kids for EIC or just the one I claim as a dependent. Her AGI is obviously higher than mine. TurboTax is showing that they both qualify for EIC for me, but I have been told that this is not allowed.