"Wrong - Dad got the EIP pmt for the child that is now on Dad's return that Mom normally has on her return"

"Dad really didn't think he got the recovery credit for the child either."

Did you look? The Taxpayers can both access their IRS accounts to see what got issued. Remember that EIP was prepaid in advance of the tax filing for it. A 2021 entitlement was prepaid in 2021, based on a projection using the taxpayer's prior tax return on file. Since the Advanced EIP/RRC was paid out early 2021, the tax return used for making the payments would be 2019 or 2020. You now seem to indicate the Mom reported both kids.

"just because Dad has the child listed as a dependent also?"

"Just because" is a great way of avoiding that one of the parents has made an error. The second return filing with any duplicate dependent SSN will be rejected, because the SSN is already listed on a filed return. The facts and circumstances will drive which filing gets which info, but these Adults need to figure out their reality. You cannot try to force the IRS to recognize reality by filing bad info.