Does Steam share DLC for games both accounts own?
If account1 has access to the GOTY DLC already, you will not have access to the GOTY DLC on account1 once you activate the base game on account1. Account2 will not have access to the new DLC if account2 is the account sharing the base game. On http://store.steampowered.com/promotion/familysharing, it says:
So, unfortunately, it looks like you cannot share DLC if the account that is being shared to has the base game or activates the base game.