Is it considered a sin to distance oneself from a Muslim neighbor to avoid potential discord and problems, and is it advisable to interact with her despite warnings?

There is no harm in not accompanying or associating with a neighbor if one fears their harm. This does not contradict maintaining good relations with them and being kind to them, advising them to abandon evil, and enjoining them to do good. This is what the questioner is advised to do if she confirms what has been spread about her neighbor.