my daughters mother claimed her on her 2019 tax refund, and got the stimulus payments for her. i did not have any income and only used the non filer form for the stimulus, where I didn't realize I was suppose to add dependents so I did not get stimulus amounts for my 2 sons, no one did. this year I am claiming all three of my kids. the system is correctly adjusting the amount for my 2 sons but it is also trying to give me the recovery rebate for my daughter.
The stimulus money you get for claiming your children is based on your 2020 tax return. When they hurried to send out checks last year they could not wait for people to file tax returns so they used either 2018 or 2019 information that was in the system already.
But the credit was an advance on a credit you get on your 2020 return. The way it worked means in some divorce situations etc when parents "take turns" with claiming the child etc. a parent may have gotten the stimulus for a child based on their 2018 or 2019 return and they do not have to pay it back even if they did not claim the child for 2020. But .....the parent who does claim the child in 2020 gets stimulus for the child---in other words stimulus is being paid out twice for the same child in many cases. That is how they wrote the law.
You do get to claim all the stimulus money for round #1 and round #2 for the children who are claimed on your 2020 tax return.