For those who claim dependents in alternating years, how will the stimulus credit affect them in 2020 if they recieve funds for them now but cannot claim them in 2020?

At this time, the IRS does not have any information available yet regarding stimulus or payment checks, which remain under consideration in Congress. You can check the IRS website for details as they become available.

the law is written very simply.  the IRS is to use the 2019 tax return and if that is not available it will use 2018 to determine your rebate. 

the $500 credit per child is for a 'qualifying child', meaning children under the age of 17 that were on that tax return.   

the law also requires the IRS to send you a letter explaining what you are to receive / have received. I imagine that will come in April at some point. 

there is no payback provision.  Once you receive the money, that is the end of the story; you will not be asked to return it for any reason. 

it's that simple.