What should a person do who proposed to his cousin, then married another woman who converted to Islam through him, and his parents and family are displeased with his action and blame him?

If you are able to marry your maternal cousin while keeping your first wife, that would be best to please your father and your family and to fulfill your commitment to your maternal cousin. If you are unable to do so, then you must honor your father and maintain ties with your family and relatives to the best of your ability. After that, you will not be blamed for their displeasure, provided you inform your maternal cousin of your inability to marry her so that the engagement can be dissolved.