Am I allowed to perform ‘umra on behalf of my mother when she is still alive?

If a living person is able to perform the ‘umra or hajj, they must perform the duty themselves. But if they are unable due to ill health, they may ask someone else to perform them in their stead and pay all the expenses for that person. But if they cannot afford to pay for the journey, they are not required to perform these duties.
It is not right to perform ‘umra on behalf of your mother. You will be much more dutiful to her if you send her an air ticket so that she could perform the duty herself. As for performing hajj or ‘umra on behalf of your deceased father, this is certainly permissible provided you have already performed your obligatory hajj.
And God the Almighty knows best.