I'd change the U-Joint if that's the problem. If yours is as bad at the post indicates it should be easy to tell. Jack up the offending side, and move the tire back and forth while watching the driveshaft, if you have a bunch of play then that's it.
As for changing it, you've gots to remove the wheel, brakes, and all. Then pull the hub (take the threee bolts at the rear out and get three more just like it but about 1.5" longer, then whack those bolts evenly with a hammer to push it out. It's going to be stubborn as hell, PB blaster will be your friend). Anyway, once you get that hub out the axle shaft will slip right out.
A big vise will be your friend now. Get two sacrificial sockets. One that is large enough for the bearing cap to fit freely in (I think I used a 7/8's, but I could be wrong) and another that's a hair smaller than the bearing cap (I used a 5/8's), use the smaller one to press the U-Joint over, with the larger one on the other end to catch the socket. Put them in the vise and tighten it down. Again you'll want to soak it in PB Blaster.
Sequoia
Oh - Another note, four letter words will help the U-Joint get out of the axle.