The quest is really simple: you just need to buy 300 stone (whether you do so with gold from the cows or not doesn't matter) and take it home with you.
Your problem with respect to the space and disappearing gold was simply that you didn't have enough carrying capacity (either through peasants or, much better, horse carriages). You can see how much capacity you have (used and available) from the bar on top. As long as your gold doesn't exceed the maximum carrying capacity (used+unused), it won't disappear. You'll find this same mechanism occur with your castles.
Hope this helps, enjoy the game!
EDIT: to get into your hometown, simply click on the large image to the right. If you want to transfer things or people, just move (very) close to your town and click the arrow symbol that appears.
Last edited by Nazar : 08-31-2013 at 08:20 PM.