There is a TSB from Hyundai for the delayed shifting. Take it to a shop and ask them to follow the procedures according to the TSB# below. Here is it:
A/T - Harsh/Delayed Reverse or Drive Engagement
Group: TRANSAXLE
Number: 07-40-009-1
Date: SEPTEMBER 2007
Models:
1999 - SONATA
2001-06 - ELANTRA
2001 - SANTA FE & XG
2003 - TIBURON
2005 - TUCSON
2006 - AZERA
2007 - ENTOURAGE
Subject:
AUTOMATIC TRANSAXLE HARSH AND/OR DELAYED ENGAGEMENT INTO DRIVE OR REVERSE
This bulletin supersedes TSB 07-40-009 to correct OP Time.
DESCRIPTION:
If you are diagnosing an automatic transaxle with a harsh and/or delayed shift into Drive or Reverse, follow the Diagnostic Procedure shown below:
DIAGNOSTIC PROCEDURE:
1. Check the ATF level when the engine is idling in "N" according to TSB 06-40-016. Adjust the ATF level as needed.
2. Perform the adaptive learning by shifting from Neutral to Reverse and Drive, stopping in each gear for 5 seconds. Repeat 10 times.
from here on it needs a diagnostic computer.
Zee