If that car has a 3 speed automatic, one strong possibility is that the T.C.C. (torque converter clutch) is locked up.
I don't remember where it is, but you could disconnect the electrical plug for the T.C.C.
It is not real hard to locate, but I dont remember the exact locale.
If the car now runs normal, as in, NOT dieing when you put it into gear, and all this shuddering, then that means you have a bad TCC solenoid in the transmission.
But if it IS bad, you can maybe fix this yourself for about $50 (ain't priced them in a while)
On the side of the trans, there is a squarish pan that the TCC solenoid is hidden under.
The pan is opposite of the side of the engine with all the belts
On some cars, it is not very hard to remove that, and on other cars it is next to impossible. Make sure and have a new gasket ready to go before you remove it.
You may have to splice the wires for the new one, but if I remember correctly, they are color coded anyways, so not too difficult.
You will have to get under the vehicle to do this repair. (do not forget to use actual jackstands and not rely solely on the crappy scissor jack)
The last car I did this on was a Chevrolet Beretta with a 2.8 V6 (not 3.8 or quad 4), I forget the year of the car. 1989 maybe? It was years ago.
And no, this problem will not activate the SES light.
They may be right about the fuel system, but what I have listed is a very simple way to check the TCC and possibly eliminate that as a problem.
FACT - this TCC I mention on the 3 speed automatic for GM cars, it is notorious for going bad. If you take the car to a shop, they are going to want to rebuild the whole tranny, you can save that cost and hassle by doing this repair yourself.
ALSO - just because they rebuilt the tranny does not necessarily mean they replaced that solenoid. Some repair shops just rig it up without doing a quality rebuild. So you may have the old solenoid still in it.
1999 LeSabre, 3800 series II engine.