If they fall in love, it won't necessarily make it Stockholm syndrome though. It is all about the reason why they fell in love and she doesn't seem to be in danger and can take care of herself perfectly fine, so I don't think stotckholm will be a thing. The princess' feelings, huh, it is not like I don't care, but her attitude makes it hard, she is not really that likable to me, but I think her behavior is understandable. I don't believe her attitude towards the prince is fair though, the guy hasn't done shit to her(let us agree to disagree here). 
There is no way the story won't have these two together, so you might not like how it is executed though.