Is a relationship with a suitor rejected by the family, which involves meetings and exchanging gifts, considered forbidden and a betrayal of the family, despite the young man's commitment and the girl's desire for him, and her belief that he is the right husband for her?

This relationship is one of Satan's means to lure you into what is impermissible. Religion prohibits such relationships outside the framework of marriage, so you both must desist from it. If the young man desires you, let him propose to you through your family and seek help from people of goodness. There is no harm in supplicating that Allah unite you as a married couple if the young man possesses good character and religious commitment. We advise you to perform Istikhara (prayer for guidance) and consult with people of sound judgment.