No. A dependent cannot have a dependent of her own. A child can actually be the Qualifying Child of more than one relative in the household. You are allowed to decide between you which one of you will claim the child. It may be worthwhile to prepare returns both ways and see which way the family comes out best. If you can’t agree, the IRS rules say the child’s parent gets first choice.
That said, there is also a rule that says if a person qualifies as a dependent, she is not allowed to claim herself or a dependent of her own.
