Is what I said to my mother-in-law—regarding covering her 'Umrah expenses if I secure a job—considered a vow, and must it be fulfilled at any time despite numerous financial obligations?

The aforementioned wording is not considered a vow (nadhr (definition)) because it does not indicate an obligation to perform an act of worship (qurbah). Rather, it is a promise that is praiseworthy to fulfill, and the questioner will have a great reward if she fulfills her promise.