How can a girl convince her family to approve her marriage to a committed young man, despite the difference in madhhab and nationality, especially after her sectarian conversion and her conviction in it?

We advise you to supplicate and humble yourself before Allah to grant you marriage to this young man if he is good for you, along with performing Salatul-Istikharah (prayer for guidance). You should also be mindful of Allah and content with what He has destined for you. Take available steps, such as speaking with the closest members of your family to this young man, or have the young man ask influential people in your family to speak with them to persuade them.