Was he eligible to claim them in 2020 too or was that her year to claim them? Did he claim them in 2020? Why do you think you need to amend the 2020 because of the stimulus?
If it was not his turn to claim the kids in 2020 and he did not claim the kids, then you should not amend the 2020 return.
If he claimed the kids when he should not have claimed them or if he did not claim them when he should have claimed them, then yes he should amend his return.
For 2021, you can file the 2021 return before or after you file the amended 2019 return. Amending your 2019 return will not affect the 2021 return. The 2020 return will not affect your return either. Each year is filed individually.
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