I believe she wanted to get power as soon as possible to cover him since he's considered a commoner therefore weak to Nobility, so if he gets into a mess due to a Noble, it's most likely that the Noble will blame the issue on him. So she's essentially trying to raise his status as best as possible to increase the protection from Nobility. If he gets married to the Duke then he will be essentially be able to dissuade the nobility from pursuing him publicly and avoid a lot of resets. And I believe the marriage idea was a last minute add on when the Duke said that he was her type. She still has the save file of when "Uncle" offered to adopt her as a back up if things go wrong in the current save.

I don't like the fact that she sacrificed the opportunity she had to became his daughter. She can just think other plan to protect his father without the need to match him to the duke. I feel like she just playing the life of people around her, well I know she suffered enough but...