96 lumina transmisssion / engine light on

My 96 Lumina APV, 3.4L, has 300K, all highway. I am looking at new one, but I need to know what is wrong.
Engine light on, when cold reverse at first does not engage, but then soon after works. When accelerating, especially uphill, front end starts to vibrate, when I let the gas off it stop shaking. Took it to dealer, and the code said either the transmission or the oxygen sensor. Apparently, tranny fluid smells slightly burned. I changed it at 250K. Then the engine lights goes out and and does not seem to shake when under load. I wouldn't be surprised if I need a new tranny; it has been a great van. Thank you.

Your transmission problem sounds like the torque converter isn't unlocking. It's similar to trying to accelerate a car with a manual transmission from too high a gear without using the clutch and/or downshifting. The engine is lugging, and can't pick up speed without the converter unlocking and allowing a little slippage. A very common problem on high mileage transmissions. The other code, although possibly valid, is unrelated. The oxygen sensor would have little or nothing to do with a transmission shudder. The only way they could be related is if the oxygen sensor is totally shot and the computer isn't adjusting fuel delivery when you step on the gas.

Thank you Richtazz.

Do you think that the transmissions will fail suddenly or will it get worse progressively? My wife is totally stressed out, because the engine light is on, and she knows that the transmission is going to go sooner or later. Of course, I am not, because I don't drive it. But I have to reassure her. Thank you again.

Knowing the exact code here would be of some help.