Total War Campaign Lan?

Not sure about Lan but...

Total War Shogun2 is the only Total War game that has PROPER coop campaign. The others only allow you to FIGHT as the AI and not together.

Spent hundreds of hours with my cousin on coop Shogun2, you can totally work and play together. Defending a castle together against the AI is a blast

Google has been unhelpful in my current search, so I thought I'd ask you guys.

I want to play a campaign mode of Total War with my wife, but I'm not sure which game to get.  I have Empire, Napoleon, and Shogun 2, but I'm open to other options.  I'd prefer to play lan if possible to get rid of any potential lag...graphics are nice, but I really don't care that much on this one.  I would like my wife to be able to battle, as well as do all the "civ" type stuff around battles.

There are so many total war games out, and lots of confusing threads out there.  Can you guys help out?  Again...I want battles and the turn based parts in a full campaign for my wife and I to play, preferably in LAN.  Thanks!

If you don't mind spending a little more money, Medieval II has an unofficial "retrofit patch" that lets you play the campaign hotseat, but fights between you and another player are just auto-calculated i think.