Turns off when switching gears?

Hi, my car starts fine and I just got an oil change. The problem hasn't been fixed and I had a mechanic give me a diagnostic report and it had nothing drastic on it. But my car usually shuts off if I switch to drive or reverse. It stutters and coughs before dying but sometimes it takes awhile to start it back up? If I step on the gas and keep the gas going it doesn't seem to be a problem but if I stop at a red light it sometime shuts off. Changing gears makes the car move and it feels very unsmooth. You can see the rpm bounce up and down when its in drive with the break before it dies also. After it has been running or awhile the problem doesn't exist but I'm wondering if a simple tune up would work? Maybe the spark plug or something has trouble warming up? My service engine light has been on but it always is. My last oil change was a bit overdue also if that has any importance. I hope this sums it up, if there are any other questions feel free to email. Thank you so much for your help!