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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There is no problem in performing Hajj with your mother with her money; rather, this is part of being dutiful to her.
The debt that prevents from Hajj is the debt in which the following conditions are met:
First: that it is due. If it is deferred, the only condition regarding it is not favoring going to Hajj over repaying it.
Second: that the lender does not give him permission. If he gives him permission, there is no blame if he performs Hajj even if this leads to delay in repayment.
Third: that he does not have money that suffices for repaying it. If he has enough for repaying it, there is no problem in his Hajj even if the lender does not give him permission.
Fourth: that Hajj is with the money of the person himself. If another person pays for his Hajj, there is no problem.
May Allaah reward you for your keenness on righteousness and your knowledge about the rulings of the religion.
Allaah Knows best.