Does the trailer imply that he was crying about what he just did, or a realization that he just torpedoed his political future?
There are two scenes in the trailer which imply that he regretted what he did. The first scene clearly implies regret, but the second one, the crying scene, did not have context to answer your question.
However, he didn't really torpedo his political future, only his presidential ambitions. He never really paid any price for taking Mary Jo's life. He could have saved her simply by going to one of the nearby homes for help, but he didn't even bother. In my mind, that makes what he did 2nd degree murder.
The trailer includes one brief scene that shows him under water trying to get her out of the car. That didn't happen. We have only Ted Kennedy's word for it, and there is no way anyone could believe it considering everything else he did that night.