Answer
In principle, it is not permissible to carry out an action on behalf of another person if such an action require selfsacrifice coupled with monetary expenditure, like Hajj, etc.
However, we suggest you perform Umrah. Thereafter, convey the Thawaab (reward) to your elderly mother. (Shaami vol.2 pg.599; HM Saeed)
and Allah Ta’ala Knows Best
Mufti Ebrahim Desai