What is the Sharia's opinion on the ruling concerning a man proposing to a woman who does not desire her current suitor, and wishes to marry the second suitor, but her father refuses the second suitor, acting upon the hadith: "None of you should propose on top of the proposal of his brother"?

You are not permitted to propose to the aforementioned girl, because it appears from the situation that she has accepted her fiancé, even if that was to please her family. Therefore, you must cut off your relationship with her until she breaks off her engagement. At that point, there will be no harm in you proposing to her. If her proposal does not materialize, then seek someone else, and do not tie your marriage to a specific woman. Allah knows best where the good lies. Allah Almighty says: "And perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not."