Is it permissible for working spouses to share the cost of the Aqiqah for their children?

The 'Aqiqah is a confirmed Sunnah for the father, and it is not obligatory for the mother or the children. If the father is poor, there is no sin upon him. If the wife wishes to assist her husband with the cost of the 'Aqiqah, there is no harm in that, by gifting him the money so that he may purchase the sacrifice.