Is my refusal to go for 'Umrah with my mother considered disobedience ('aqūq) and a sin, given that she has sufficient funds for 'Umrah but not for Hajj, and I cannot cover the remaining expenses, in addition to my belief that Hajj is more obligatory for her?

If your mother has not performed the Hajj obligatory ritual or Umrah before, then it is more proper for her to prepare herself for Hajj, and she should be urged, persuaded, and helped to do so. She may perform Umrah with Hajj or after it.

If your mother insists on going for Umrah and wants you to accompany her, then you must obey her if you do not have a valid شرعي (Shar'i) impediment, as she takes precedence over what you save.

It is not obligatory for the mother to save money for Hajj; rather, Hajj becomes obligatory upon her if she is able and has no impediment. She may perform Umrah repeatedly even if she has not performed Hajj. Scholars have unanimously agreed on the permissibility of performing Umrah before Hajj or Hajj before Umrah.