Your troubles can be over with, with less than a $150 fix...admittedly the rear shocks on our cars are...junk. From another forum I am a member of, we are and I have already done so, replacing the rear shock absorbers with KYB #554384
Gas-A-Just shock absorbers. They totally smooth out the Elantra's skipping and rough/unsure feel on rough roads and highway/freeway bumps that plague our Elantras right from the get go. These shocks make a WORLD of difference in the way the Elantra not only drives, but takes bumps and ruts and highway expansion joints and all that! It will feel like a different car ALL together, especially at highway speeds. I bought mine from Rock Auto for $62.50 a piece, and WOW! You will love these people...don't even mess around, get the KYB's!
"Pimpin ain't easy,but it's better than living out of your wallet"