Is it permissible to consider the amount I will send to my mother to cover the expenses of her Hajj as part of my Zakat?

Hajj is not obligatory for the mother if she is not financially able. Scholars differed on the permissibility of paying Zakat (definition) to enable the mother to perform Hajj. The majority of them went to the opinion that it is not permissible, and that "in the way of Allah" is specific to Jihad. However, there is an opinion by Imam Ahmad, chosen by Sheikh al-Islam Ibn Taymiyyah and the Permanent Committee, which permits it. If you adopt this opinion, it is permissible for you to enable your mother to perform Hajj from your Zakat money. Nevertheless, it is more cautious not to count this as Zakat.