All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Being kind and dutiful to the mother is one of the greatest acts of worship by which one seeks nearness to Allaah and which could be a reason for being saved from Hellfire and being admitted to Paradise, Inshaa' Allaah. Therefore, in our view, you should give priority to Hajj of your mother above being charitable to your married sister for two reasons; firstly, to be kind and dutiful to your mother, as we have previously mentioned, and secondly, some scholars are of the view that it is an obligation on a person to send his parents for Hajj if he is able to do so and if they are financially unable to afford it. It should be noted that if you can afford to do both [to pay for the Hajj of your mother and give charity to your sister] then that is indeed two good acts. Spending in charity wipes out the sins in the same manner that water extinguishes fire. The Prophet said: "Giving charity to the poor is (rewarded as) a charity (only), but giving it to a relative is (rewarded as) a charity and keeping ties with kinship." [Ahmad and At-Tirmithi]
Allaah knows best.