Can a child be claimed as a dependent on income tax

Probably not but I don't practice tax law so wait for further answers from someone who does

In order to claim a child as a dependent, that child has to live with the taxpayer for more than half of the year, and the taxpayer must provide for more than half of the child's financial support. There are other factors that have to be met, but given the scenario that you've described, I would think that one or both of those factors would prevent the parents from claiming the child as a dependent in this particular case.

It's a difficult question. The rules for children qualifying as dependents may not apply, but the rules governing dependents in general might. And I'm not sure on the rules applicable to children. This generally comes up in the context of either divorce or children in college. My gut is that there should be a way to justify claiming dependent status.