Is it permissible for a son to perform Hajj with his mother as her mahram, given that the mother wishes to perform Hajj and the son cannot afford Hajj at his own expense, and the son desires to perform Hajj?

It is permissible for your brother to perform Hajj at your expense and be a mahram for your mother during the journey to Hajj. You will be rewarded for this by assisting your mother with Hajj and by having your brother perform Hajj at your own expense.