bad tires can shake pretty bad so you can rotate them to see if they get better.
Also this tech service bulletin.
VEHICLE MAKE/MODEL: MODEL YEAR(S):
MANUFACTURER: Hyundai Motor Company
MFR'S REPORT DATE: April 14, 2009
NHTSA CAMPAIGN ID NUMBER: 09V124000
NHTSA ACTION NUMBER: EA08016
POTENTIAL NUMBER OF UNITS AFFECTED: 175765
Ther stabilzer bar and bad bearing are the other thing loose lug nuts. I know you have check that already but some dont.I have done a bit of extra check and want to supply you with evrything. so here is a pdf on a issue your hyundai has
http://www.mediafire.com/?ni2yynu22nz If they have torqued your wheels down wrong your rims may have issues there is a special way to do that too.
It just happened again. It almost feels like there is a transmission is slowing the car down. After it happens even at lower speeds it feels like the transmission is slowing the car down.