Is it permissible for a woman to travel with her maternal aunt's husband within the country for a short distance (masāfat qaṣr) for a need related to master's studies, in the presence of her mother or his daughter, given the absence of her original maḥram and her need to preserve money?

The husband of the maternal aunt is not a mahram, so it is not permissible to be alone with him, nor can he be considered a mahram for travel.

Regarding travel, there are two issues: 1. If a mahram is available but at a cost and with difficulty: If completing the study is not essential, or if the expenses are bearable without hardship, then travel is not permissible except with a mahram, due to the absence of a necessity that would permit what is otherwise forbidden. 2. If the travel is safe with trustworthy and righteous company: Most scholars do not permit a woman to travel a distance that allows for the shortening of prayers (qasr) without a mahram, except out of necessity. This is the preponderant view. However, some scholars have allowed it in such a scenario if safety and protection are ensured, such as the presence of trustworthy company including women, or a short-duration journey on a populated route. They base this on the reasoning that the cause for prohibiting travel is the fear of fitna (temptation/strife), so if this cause is removed, travel becomes permissible.

And there is no harm in adopting the easier of the scholarly opinions when there is a need.