Am I permitted to move and live with my husband in the South, even though the marriage contract stipulated settling in the North, and despite my parents' anger at my husband for not fulfilling his promise and for refusing to answer their calls, especially given their difficult health condition?

The condition agreed upon for your stay in the north is valid and binding. If the husband violates it, you have the right to annul the marriage. Fulfilling this condition is recommended, but not obligatory, according to the Hanbalis, so the husband does not sin by violating it. However, Sheikh Taqī al-Dīn inclined towards the obligation of fulfilling such conditions. The husband's retraction from the condition is permissible according to most scholars, especially if it is for the sake of his mother's well-being. The husband's obedience takes precedence over the obedience of parents in this matter. You should honor your parents and seek their رضا, and the husband should assist you in this with kindness. The husband's desire to marry another is permissible if he is capable of being just, and he may forgo this desire if you agree to go with him.