I just had the same problem on the highway i could feel it swaying when i turned or gunned it.thought my daughters hit a curb or something anyway long story short i just replaced the back tire and when the guy went to put the tire on the whole dam thing was wabbling (tire on) so its the wheel hub bearing

 

Turns out it was my differential. Most likely caused by a failing center carrier bearing and failed differential bushings. Also prolly due to a bad differential. Replaced all. Found a replacement from a 2005 for a hundred bucks on eBay. Swapped out the bearings and it's smooth sailing.