Is it permissible to separate from a fiancé with whom matters have become difficult after the marriage contract due to the long distance and people's talk, and the existence of another suitor who might be a suitable alternative?

What your neighbor did by inciting your husband to leave you so that she could marry you to her brother is forbidden and impermissible. This is because merely hinting at a proposal to a woman in revocable 'iddah (waiting period) is not permissible, so how much more so explicitly proposing to a married woman.

This woman must repent to Allah. You should not pay attention to her, but rather be patient until your husband is able to bring you. If waiting for him becomes difficult for you, then consult with your family about separating from your husband through divorce or khul'. If that occurs, then there is no impediment to your marriage to your neighbor or anyone else.