hmmm, my first instinct is that you have a plug that is getting fouled due to a misfire while underload at low RPMs since you have an automatic and it clears up when you put it into park after 10-15 minutes. Question, if you were to turn the car off immediately upon the bad idle and start it back up, does it go away or does it still need 10-15 minutes of non-loaded idle to clear up?
Second thing that crosses my mind is that your alternator or battery may not be up to snuff and putting out enough voltage to keep the ignition system running under full power. Test your voltage output on your alternator and across your battery while in park and in drive (DON'T USE YOUR PARKING BRAKE FOR THIS, get a friend to hold it in drive and STAND TO THE SIDE!
Slade