York's sons help him out by killing anyone who threatens York's bid for the throne. We only see them briefly at the end of this play, but it's long enough to watch Richard kill Somerset and fulfill the prophecy about the castles: Richard notices that there is an alehouse sign with a castle hanging over the dead guy's body. Now, that's what we call kind of creepy.
We don't really get to know Edward or Richard in this play, but we certainly will get to know them later on. If you want to see these future kings in action, check them out in Henry VI, Part 3 and Richard III.