This is an idiom. Being "under" her vows means that she is committed to them and that they are still in effect. Alternate translation: "while she is still committed to those vows" (See: [[rc://en/ta/man/translate/figs-idiom]])
The word "obligations" can be expressed with the verb "obligate." Alternate translation: "the things she has obligated herself to" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])