Are the wife's family entitled to claim alimony for the suspended daughter, given that the husband has not consummated the marriage after discovering manipulation in her real age?

If it becomes apparent that the wife's stated age differs from what her family declared, and this constitutes deception and falsehood, then you have the option to annul the marriage, because age affects people's desires. The husband has the option [to annul] for any defect that is customarily considered a defect, if safety from it was stipulated, even if it was based on the description of the woman's guardian.

If you choose to annul the marriage before consummation, nothing is binding upon you, and the wife's family has no right to demand half of the named mahr (dowry), because whoever has the option [to annul] and annuls before consummation owes no mahr. It is not permissible to leave the wife in limbo; rather, you must either hold onto her honorably or release her kindly.