Even though you told TurboTax the other parent was claiming your child, that refers to Dependency only.
You can still claim a non-dependent child for the EIC, if you qualify to.
After fixing your Rejected return and Efiling again (and being accepted), be sure to wait until you receive your refund before filing an Amendment.
You are right, however, that your accepted return should be the one you are Amending.
If you're using TurboTax Online, try canceling your amendment, close the program, and then clear your Cache and Cookies and retry amending.
In TurboTax Desktop, it could be that your fixed original return created a new file, so you may see two files when you open the program.
If this doesn't resolve your issue, since we can't see your return in this form, I would suggest that you screen-share with the techs at support. Here's how to Contact TurboTax Support.
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