It's been awhile since I've played, but I seem to remember some rule of thumb being that when you become stuck in the woods, just keep heading down until you reach one of the exits. There should be more than the two ways out that you mentioned and I think there's even a scene that will eventually take place where the parents come into the woods and find you, telling you to get home, which then removes you from the area.
Found this on a wiki for the game:
To get out of the Lost Forest without getting grounded, follow this path:DOWN, DOWN, DOWN, DOWN (GO SOUTH 4 times).
If you want to get grounded (why would you?), go into the Lost Forest and don't move for a couple of minutes. Walk into any direction one more time and your parents will ground you for getting lost. You'll get sent back to South Park.