Is it permissible to perform Hajj on behalf of a deceased mother who was 74 years old and was unable to perform the obligatory Hajj during her lifetime?

It is not permissible for your mother to appoint someone to perform Hajj on her behalf as long as she is physically capable of performing it herself. The prohibition due to age restriction is not a permanent incapacitation. Appointing someone else is only for those whose incapacity is not expected to cease. She must wait for the impediment to be removed, and there is no sin upon her for the delay due to her inability at present.