I really like that Elsa is going to try and earn Yvonne's dad's approval. Earn. Fantastic. Other authors, writing a similar story with lesbians trying to get approval from parents, would just call the dad homophobic or a bigot. Then the story would show how stupid and evil he is. Then humiliate him. Then he would either die or have some other bad ending. Or if he reforms, he would have to do it while groveling and begging for forgiveness. Which is basically just immature and childish wish fulfillment, and terrible story writing, from those authors.
This author though, is one of the very select few, that has written a believable, emotionally mature, and complex character for the dad. When you're trying to change someone's mind, it's not something you magically do in the course of one conversation. It takes time and effort. It's earned.
I also like how the author is showing the dad's thoughts and emotions, and how he's gradually changing. Like his daughter, he's stubborn, and seems like a tsundere. He feared losing his daughter to her eventual husband. But now realizes that he's not losing her. He's instead gaining a 2nd daughter. I suspect that Elsa' powerful and skillful use of magic will clear the last concern he has.