Is it obligatory for a betrothed woman to break off her engagement because she is compelled to travel with her fiancé to another country, leaving behind her elderly mother who needs her care and has no mahrams?

If you can combine marriage with staying with your mother or moving her in with you, that would be preferable. Otherwise, do not move away from her, even if it leads to breaking off the engagement, provided that marriage is not obligatory for you. Perhaps Allah will compensate you with something better and reward you for your dutifulness to her.