Hm. Well, the checks are based on your 2018 tax return, so I don't think there is really anything you can do about it.
In turbotax, what you would do is list the child, check "all year" for how long they lived with you, and then answer "yes" to "will you allow the other parent to claim the dependent exemption using form 8332?" This would include the child in your household for purposes of EIC and certain other tax benefits without claiming them as a dependent. However, I just don't know if this information is transmitted to the IRS or not. It certainly can't hurt to add it.
Separately, you don't say why you don't claim the children. If it is a custody matter, and you have not been giving the other parent a signed form 8332 every year to allow them to claim the child, then they have probably been filing as if the child lived with them full time, in which case any credits based on 2018 might be screwed up. You could file an amended 2018 return but it won't be processed in time for the issuing of the emergency checks (assuming the law ever passes) but you would correct the record and maybe fix things going forward.
If this is a custody situation and you don't know what a form 8332 is, reply back for more details. (And it may help to give us some of the details of your own specific situation.)
