Hyundai Repair: Timing Belt Replacement?, timing belt replacement, wheel balance

Question
I have a 2003 Sonata with 63,000 miles & the dealership wants to replace it for $500.00. This one is a V-6 and I have read that they have had good luck with that engine and the life of the timing belt...Should I replace now or later?
Also, they just did an oil change and rotation of tire and now my steering wheel shakes like crazy...back and forth quickly all the time...not at increased speeds. Any ideas? No problems before this with the car. Thanks!

Answer
Whether you should replace the timing belt now or later is a decision you must make.  It's true that I've never seen a timing belt on this engine fail within the maintenance interval.  But I also cannot tell you when it will fail.  Your chances of having a problem right now are miniscule, but as time goes on, the chances continue to get greater.  It all amounts to how you wish to hedge your bets.  Replacing the belt means $500.  If you wait too long before replacing, it probably means thousands of dollars in engine repairs.  Either way you look at it you've got consequences: $500 now; possible engine damage later.  

If the vibration started when your tires were rotated, I'd expect that you have some sort of problem with the tires now on the front of the vehicle.  Could just be wheel balance.