Is it considered disobedience (ʿuqūq) to a parent if one does not invite the elderly father into the home, and instead opts to meet him outside to avoid problems with him and his beliefs? And what is one’s duty towards him, especially given his hatred for the husband due to the latter’s opposition to his ideas?

Despite the bad thoughts and actions attributed to your father, being dutiful and kind to him remains obligatory. It is sufficient to inwardly dislike his objectionable actions without any verbal or physical abuse. It is not an act of disobedience to not invite him to your home out of fear of problems. Among the greatest forms of dutifulness to him is striving to reform him with patience, repelling his abuse with kindness, and supplicating for him with prayers. Never despair of him. Continue to advise him as long as the reminder is beneficial. If there is a fear that advice might increase his stubbornness or lead to greater harm, then it is better to desist. Exert your effort gently, especially since he is elderly, for you might be a cause for his guidance, and that is a great good.