If a child lives in your home more than half the nights of the year, they are a qualifying person for HOH and they are automatically your dependent. You can release the dependent to the other parent if you give them a signed release form 8332, but they are still a qualifying person for HOH, and can never be a qualifying person for HOH for the other parent, even if you release the dependent claim. That's what the "not a dependent" status is all about.
You should be answering, "yes the child lives with me" and "yes, I will give the other parent a form 8332." The other parent should be answering, "no, the child does not live with me" and "yes, the other parent will be giving me a form 8332." In that case, the child can be listed on both returns and not cause any conflicts with the IRS.
It's possible the error is caused by your ex claiming your child as if your child lived with them, instead of using the release. That's on your ex, not Turbotax. As long as you prepared your return with the correct information, you can print and file by mail since e-filing is blocked. If ex claimed the child the wrong way, both of you will get a letter from the IRS and you will need to explain the situation.
