Yeah. In regards to the underlined bit: That's the problem I, myself, see in my own idea. I was hoping that by posting it, someone would have a brilliant idea to fix it; we have many brilliant minds on this forum, after all.
Well if it's ideas you want, I can think of a couple (which isn't to say I like 'em):
1) The second city exists on a separate plane. It is not built, but is instead transported to this realm.
2) The second city is conquered, and you get access to its areas/resources after invading each individual section and capturing it. (This could actually be pretty cool if, for example, one section of the city contained a Mage's college and you had to work your way through the school defeating various challenges. Big challenge, big reward.)
3) The second city is run by Protoss, and they phase it in bit by bit.
4) The city is a psychic projection of all your past lives. It doesn't exist in a material sense, and all its inhabitants are you (from previous (and perhaps future?) lives). It grows via meditation (represented by quests), and since it's all in your mind it bypasses the contradictions of growing a city overnight. (What can I say, I'm a solipsist, remember?)
*Edited because I left off an ').' Yeah, I'm a little anal.