I know right? he leaves his son with a random old man -.-
Actually, that's a time honored tradition here on Earth; though usually it's done by both sides as part of a peace agreement. Each side give their heir into the custody of the other, basically exchanging hostages to ensure good behavior. After all, Balgruuf isn't going to start anything if it can get his children killed. Heck, that's probably the
only thing keeping him from marching into Whiterun and challenging Vignar.