No. The special rule is only for the parents, and they must not be living in the same household.
In the case of a grandmother, mother and child living in the same household, either the mother or grandmother can claim the child. The grandmother must have a higher income, than the mother, to do so. Whoever claims the child claims the child tax credit and EIC (and dependent care credit, if applicable). The other can claim nothing. Whomever's home they are living in can claim HoH, but only if she has a qualifying dependent.
