You are likely going to have to print and mail your return as you won't be able to e-file.
While you can agree to allow the other parent to claim the child as a dependent, only the custodial parent (one the child spends more nights with) can claim the child for Earned Income Credit (EIC), Child and Dependent Care credit (CDC), and Head of Household. You cannot "shift" those via agreement. You can, however, shift the dependency exemption and the Child Tax Credit.
So, if you answered the questions to indicate that you are the custodial parent then only you are entitled to the EIC, etc. Now, this scenario can cause problems with the e-file system because the child's SSN remains on your return in these scenarios as it is still your right to claim the EIC/CDC/HOH. What is happening is the IRS e-file system is hypersensitive (due to general ID protection measures) and it will still read the child's SSN on your return, even though you are not claiming the child as a dependent. And, thus, it will reject either your return or the other return.
So, the only way forward is for you to print and mail your return. You could remove the child completely in order to efile but this could cause you to lose substantial refund (or increase taxes owed) if you are getting the EIC/CDC/HOH. When you file by mail, the IRS will still process your return and pay any refund due, even though the SSN is on both returns as it is legal. It is just the e-file system itself preventing you from filing.
