Is it permissible for me to seek permission to go to my father's house and inform him of my departure from the home and request a divorce due to my husband's repeated customary marriages, his travel to countries I warned him against, his change and avoidance of me, and his lying to me, even though I lack nothing?

There is no objection to visiting the parents' house with the husband's permission; otherwise, no, unless there is a legitimate excuse. Seeking divorce is forbidden unless there is a valid reason. A husband marrying another woman does not permit seeking divorce, and she has the right to demand justice, as this is not betrayal. If she dislikes her husband and fears falling short in fulfilling his rights, she may seek khul' (divorce at the wife's instance, by giving compensation to the husband); however, it is preferable to wait until the benefit of separation becomes clear.