Definately not an alignment issue. You shouldn't be focusing on alignment if the problem is shaking at speed. Bad alignment would show symptoms more like the car having a bias left or right, and bad tire wear.

At first glance, I would say have the wheels balanced again, b/c sometimes when they get balanced the guy doing it is having a bad day er' something (seems to happen EVERY time I get my wheels balanced, I notice horrible shaking immediately afterwards and have to take the car back again to have it redone) BUT>>> the fact that you said you can feel it clicking AS YOU TURN- that sounds pretty major to me. I'm thinking it could be anything from the differential to a misbalanced drive shaft. What do you guys think???

Ball joint recall related? Hmmm, did you immediately notice it? I'm drawing a blank on to how they could have messed up there and caused shaking.