Is this considered a proposal on top of a proposal, taking into account the girl's rejection of the first suitor and her opinion not being considered in marriage in her society?

The authentic Sunnah of the Prophet prohibits a man from proposing to a woman who has already accepted another man's proposal. This applies when the woman has inclined towards the suitor and accepted him. However, if she has not accepted him, it is not forbidden to propose to her. So, if this girl did not accept the proposal, it is permissible for you to propose to her. If her family is complicating the matter, you can seek a way to convince her guardian to marry her to you, and explain to him that it is not permissible to force a mature, sane adult woman to marry someone she does not wish to marry. Otherwise, she is permitted to raise her case to the Sharia court for the judge to consider the matter and marry her off, or appoint someone to marry her off, if it is established that her guardian is unjustly preventing her marriage. If you are unable to marry her, then look for someone else.