Don't go hard on him, but don't go easy.
When you're dealing with any questions or comments from him, you need to invest more energy when dealing with him. Make sure you hold your ground and all that, but be prepared to take a little more time in dealing with him.
But for clothes, you've gotta do what you've gotta do. If this is your big sort of coming out celebration, it may not rise to the level of a wedding (bride), but it's upward of a coming-of-age type event (cotillion, quinceañera) or at least prom, bridesmaid, or wedding guest. Dress up for that as you see fit, neither giving in nor feeling you need to make a point. I could see a tiara being overkill simply because most of the women I've known a long time have never worn a tiara for anything (other than maybe for dress-up as little girls), but if it's important to you (rather than something you're on-the-fence about), wear it. I think the important thing may be sure your outfit is in "good taste" and doesn't enter into gaudy (going over-the-top with jewelry, especially gold) or suggestive territory (avoid low-cut and high-slit things, just because most fathers would disapprove of that in their daughters anyway), but I believe your dressing sensibilities probably put you in ~safe territory anyway.
Your dad also has the option of not being at the party. It's not ideal, but it might also maximize happiness of everyone (including him) involved, although it is probably less desirable in the long run.