I wanted to schedule a chapter for later today, but it ended up posting 12 hours early...

So I tried to delete it by clicking the little trash bin icon, but, other than changing to a refresh icon, nothing really happened. The chapter didn't disappear or anything.

How do you delete it completely so that you can reschedule it? Or is there a simpler way to directly reschedule without having to delete and repost?

Deleted chapters are invisible to anyone that isn't the author. If you schedule the same chapter (from a draft, for example) it'd get posted when it is scheduled to, and you'll end up with 2 versions of the same chapter, one that only you can see, and one that everyone can.