She doesn't want to be queen for the sake of being queen or because that was her goal, being queen isn't the goal for her it is the path and the tool to achieve her goals which are bettering the lives of the common people as they the backbone of nobility and what makes a country worth, her position as a duke daughter won't allow her to make political moves and laws to change the nation for the best, as for the Prince being weak nothing she can do about it since he is the heir to the throne she may end up doing all the work but she can make him the face to her plans since it seems that the past queens were just pretty things for the crown so her words as a woman won't have much weight as the king, although I am pretty sure the prince isn't the ML.
I said what I said. She can help people without being queen
She can help and is helping the people of her territory and it seems they are better off then the people in other places, however that how far her authority reacted her own territory not the people of other nobles territories since the nobles won't heed the advice of taking care of the people and she can't force her way on others territories since that would be taken as her household trying to overtake others nobles territories and can lead to war between territories and cause her house to be charged with treason and be the end of them, the nobles won't listen they must be forced by a higher authority with is the royals only then she can help build better lives and better policies nationwide
Well dude, there's a difference between helping as a Queen and helping as Duke Daughter. It's like comparing Minister with President afterall.. The more power you have, the higher you can go, the stronger effect you have over the nation or even world
At this point it sounds like she's begging It's not giving strong It's giving "I need you to marry me and be queen because that's all I've worked to do and I don't know or don't want to do anything else". Realistically I don't see why anybody would want to marry a print especially back then. All the cheating, illegitimate children, disrespect not to mention the potential to be butchered if there's an uprising. And this Prince seems incredibly weak-willed and easy to manipulate who would want to deal with that.