I know of two companies that sell movie theater schedule datasets (through data dump or API): Tribune Media Services (http://www.tribunemediaservices.com/) and West World Media (http://www.westworldmedia.com/).
I'm not sure that there are any other. It's my understanding that the main movie sites (Google, Yahoo!, RottenTomatoes, MovieTickets…) all get their info from one of these two companies. This is also probably why you won't find a free API with that data.
Because the trailers are on YouTube, I suspected that the info was scraped from Google (I believe these two companies have their own trailer hosting); however, that would then make the connection between that info and RottenTomatoes a bit tricky… Peter, do you mind sharing?