Nothing here makes sense. Do you do both parent's returns? You cannot report the same child twice.

You used the word "non-qualifying" but is this for HOH, child care credit, RRC, etc?

Nothing here explains who qualifies for what or which parent tried to claim which provision. You didn't mention if they handled any advance payments correctly, either. Or, if one got money and the other is now trying to claim that as a refundable credit.

You state Mom has 2 children. How many does Dad have? You didn't mention if they all live together, who pays for the household? Marking that a child "can be claimed" is not the same as a child being claimed on two returns.

I recommend using the IRS wizards, one at a time for each adult and work through the provisions:

https://www.irs.gov/help/ita