Is performing Hajj on behalf of one's mother, using the husband's money and with his consent, Islamically permissible, and is the doer rewarded, or is the reward only for the one on whose behalf Hajj was performed?

This Hajj is valid on behalf of your mother if you have already performed Hajj for yourself. Otherwise, the Hajj will be counted for you. A condition for the validity of deputizing someone for the obligatory Hajj is that the person on whose behalf Hajj is performed must be in a state that permits deputization, such as being deceased or suffering from an incurable illness.

There is no harm in the Hajj being funded by your husband's money, as long as it is with his consent, based on the Prophet's (peace be upon him) saying: "The property of a Muslim is not lawful except with his willing consent."

As for the reward, it is hoped that you will receive a reward similar to that of performing Hajj, as some scholars hold the view that the reader or performer receives the reward for their action, and the recipient also receives a similar reward.