Don't count on that money anytime soon. You may not get it until 2022. Like the first round, the money will first be distributed by who claimed the kids on the 2019 tax return.
"In essence, the stimulus check acts as an advance of your 2020 income tax refund. This means when you prepare your 2020 income tax return, there will be a line to include the section 6428 credit (line 30 on the 2020 form 1040). You will get the first $500 per kid (under 17) then. It's not clear, yet, how the next $600, per kid, will work, but you may not get it until you file your 2021 return in 2022 (EDIT: see NCPerson's comment below about the reconcile being due on the 2020 return).
As others have suggested, you could file an amended 2019 return to add them. But, it's not clear that that will accomplish anything but make trouble for the other person(s) who did claim them.
