To the OP, I hope you understand that the motivation in pointing out the copyright issue comes from concern for your business. I didn't see your site but one thing that was left unsaid that should be said is that if there are indeed copyright issues, all it takes is one anonymous complaint to Google AdSense and you may find yourself banned from the AdSense program forever.
Let's consider the copyright side-topic closed from here on out, please. Thanks. :)
Back on topic: is there any way I can control the content of the ads to be more "Family Friendly" and preferable center around Disney
No, not really. The content of the ads is controlled by the inventory of advertisers pouring money into the AdSense network. From there Google can display contextual, interest based advertising, or CPM type advertising depending upon what their algorithm decides will be most profitable for the advertiser (Return on Investment {ROI]) as well as most profitable for you. In general, the algorithm controls the click price, which can float up or down depending upon things such as the likelihood of a conversion, a likelihood which in turn is calculated by taking into account statistical analyses of past transactions, context, etc., etc.
As far as Disney specific inventory, you might want to expand your content to include more destination oriented topics (Orlando, FL/Anaheim, CA), which includes flights, hotels, limousines, restaurants, etc. For better monetization it would be in your interest to consider expanding your content beyond Disney- even though the site starts out as a trivia site, there's no reason you can't expand the focus of your site. Amazon started as an online bookstore, after all. The key thing to understand is that limiting the focus of a site limits the inventory of advertising, leading to backfill-type advertising such as fat belly ads.
Good luck, bud!