If you have already filed your return, go to TurboTax and click Add a State.  That will get you back into the return and will not actually add a state.

Go back through your interview questions for the child who did not live with you.  Make sure that you marked zero months for the time that the child lived with you.  Then answer the questions about the child living with another relative and whether the other relative can claim the child.

Those answers will result in the child not being claimed as your dependent and then the child will not be included on your earned income tax credit.

You can file an amendment when amendments are available in TurboTax so that the correct information is submitted.  The other parent can then claim the child after the amendment is processed.

If the child did not live with you at all  and you are not claiming them then you should NOT have entered them in the program at all anywhere.   Amend the return to remove the child completely will correct this error.  Do not file the amended return until you get the original refund. 

The other parent will need to mail in their return this year even if you amend yours.