Will marrying a man who is already married and a father of three children disrupt his family, especially with his parents' disapproval and his own hesitation, and what should I do about my poor psychological state?

The Sacred Law has permitted a man to marry up to four women, provided he deals justly between them. There is no objection for a woman to marry someone who has been previously married. Therefore, if the man is of good religious character and moral conduct and proposes to you, you should agree and try to convince your family with what the Prophet, peace and blessings be upon him, guided to: "If there comes to you one whose religion and character you approve, then marry him. If you do not do so, there will be tribulation on earth and great corruption." However, if your family insists on refusing, especially your father, then you must honor them and obey them, as narrated in the hadith of Abdullah ibn Umar with his father Umar, may Allah be pleased with them both.