appears they will go off the 2019 tax return and if that is not there, go off the 2018 tax return, appears that will determine who gets the rebates. (and if neither tax return is there, they do have the records of who worked from Social Security to determine the $1200 part of this, but certainly not the children)
Part of the law is that the IRS is to send you a letter indicating how much you are to receive. Might be worth waiting for that letter (maybe later in April?) to assess the situation,
given the speed the law was designed and passed, it had to be easy to implement. If they were going to get involved in every permutation of consequence, Congress would be arguing about it well into next year!
