You will need to Amend each of your tax returns to make a change. Keep in mind, there are rules for claiming the Earned Income Tax Credit (EITC). See below for more details.
How to Amend?
What are the qualifications for the Earned Income Credit (EIC or EITC)?
Only the person with whom the child lived for the most number of nights during the year can claim the EIC. Are you divorced or living apart or are all of you living together?