Why would you amend? If you are the custodial parent(s) then you claim the child and mail your return. Was your 2019 return rejected when you tried to e-file it? E-filing is now closed for 2019 returns anyhow. But if you are the ones who can claim her then you MAIL your 2019 return so that it will be hand processed by the IRS.
The stimulus check is an advance on a credit you can receive on your 2020 tax return. If something went wrong or you did not get the stimulus check this year, you can get it when you file your 2020 return in early 2021—if you are eligible.It will end up on line 30 of your 2020 Form 1040.
If you are the custodial parent and/or the non custodial parent with a form 8332 then you should amend the 2019 return to claim the child you are entitled to claim. The stimulus payment is another story ... it is too late to get it now based off the 2019 amended return ... instead you will claim the child on the 2020 return to get the stimulus you did not get already.
If this is their year to claim the child then you will need to use the court system to get satisfaction as the IRS will not intercede.
here's where the Courts and the IRS differ. the IRS says the custodial parent gets to claim their qualifying children despite any court order to the contrary. the IRS says for the non-custodial parent to claim qualifying children the custodial parent must supply signed form 8332 to the other parent which that parent must include with their return. amending your return won't do any good if she's the custodian and hasn't furnished you with the form. it will be rejected since the kids have already been claimed by her. on the other hand if you are the custodian do file an amended return - eventually you'll get a refund and she will have to pay taxes, penalties and interest. what can you do if she's the custodian - see a lawyer - the IRS sees nothing improper in what she did. since she claimed them in 2019 she's likely to claim them in the future. only the courts can do anything.
Is there agreement on who is claiming the child in 2020?
If you claim your daughter in 2020, the reconciliation of the stimulus will cause you to collect $500 on Line 30. There is no need to amend 2019 tax return to make this happen. The payments in the spring was an advance against taxes owed in 2020 and the 2019 tax returns were used to figure out how much to send to everyone. But sitting here in late 2020, nothing about the 2019 tax return matters with respect to the first stimulus payment.
Mother's stimulus tax reconciliation on her tax return will say she received too much. (because the daughter is not on the 2020 return), but by law is not obligated to return the excess money.
That means that one child could cause two $500 payments to be made because of the way the CARES ACT and the IRS is administering this thing.
The same thing is going to occur with the 2nd stimulus payment because the payment will be based on 2019 data, but the reconciliation is based on the 2020 tax return with no obligation to return over payments.