Oooh. It looks like Aria is getting drawn in more by the prince now, and vice versa.
Honestly, I consider the mistaken identity to be a good thing. The prince is courting her by proxy for now, and all the gifts and affection meant for her is going to the undeserving Mielle. The prince admires her sharp wit, and Mielle doesn't have enough of it at this point to meet those expectations.
Eventually, he's going to find time to come meet the family in person and the whole misunderstanding will come to a head. Provoking the Duke's house Mielle is engaged to, being misled by an asshole family who's pushing Aria's credits onto Mielle, and the general disparity in expectations and treatment...It's pretty clear what's at the end of the tunnel here.
The family will look like the asshole, Mielle will look like a glory-hog and unfaithful girl, and Aria will look like the pitiful soul who's unwittingly being taken advantage of by her family due to discrimination. Not to mention the Prince feeling awkward about the misunderstanding and their relationship starting with her having the leverage.