All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and messenger.
Scholars unanimously agree that Hajj is obligatory only on those who are able to perform it. Allah Almighty says (what means): {And [due] to Allah from the people is a pilgrimage to the House—for whoever is able to find thereto a way.} [Quran 3: 97]
Thus, if the questioner's mother is able to perform Hajj with her own money, she is required to do so. However, if she is unable to do so and you do not have enough money to pay the expense of her Hajj, then you do not have to borrow for this purpose. In case you do and you are able to pay it off and, furthermore, it is an interest-free loan, then you are permitted to do this. We hope that your action will be regarded as a form of dutifulness to parents.
Allah knows best.