They dont have to get along fine, they just have to be in the same city. The player is essentially the council of thirteen so if they order the clans to stop fighting each other and march out together they'll do it. Also another thing from the fluff you're not taking into account is the under-empire, regardless of where the clans are based they can be moved anywhere else at the whim of the council. None of the clans are above hiring their troops to each other. Couple all this with the fact that you've only got three non-clan units and the disparity of the skavens starting settlements and I think you'll end up unbalancing the skaven in comparison to other factions who dont have the same sort of clan structure.

On the castle/city thing, they're essentially two seperate core buildings trees, the only difference I think is castle tax rates are hardcoded. The problem with having two seperate trees buildable by two seperate factions is that if one takes over the other they wont be able to upgrade it.