Vibration in drivetrain

What is the RPM while in gear? Too low and it will vibrate. Also check for weak/broken motor mounts which will cause a vibration in gear

try a simple fix of putting injector cleaner in the tank to clean the injectors
check for any loose body screws and panels

check for a broke motor mounts ore tranmission mount.

I had the same year and model car. You should check under your car for loose heat shields on the exhaust. Next would be the driveshaft and motor mounts. Check trans fluid levels.

You are putting a load on the drivetrain going uphill. There are some physics involved to get just the "right" vibration to be annoying and on your car it happens at that point.

If it has been awhile, get the Autotrans filter and fluid changed. Do not mention the vibration. If there is excessive metal chips in the trans pan they will tell you. Some wear is normal. In these Economic times shops are looking for work.

It's low on transmission fluid! It has to be checked and pumped in from the bottom of pan. Check for leaks too.

your highway acceleration problem could be a coil problem. Not sure if that year of chev has coil packs or not but experienced same thing with ford 5.4L. went through 3 coil packs and did the same thing each time before biting the dust. Transmission seems to be sticking on the 1to2 upshift and could be a sticking solenoid in the valve body of the tranny. If the shifting problem persists then the tranny deffinately has to be rebuilt. It's made it quite far if tha is the original tranny, you cant expect too much life out of it if it has been worked hard. I highly doubt a fluid change would help at all. Or if you want, you can buy a can of new truck from GM for about 25 to 35 thousand bucks! Typically works great!

Wow..thats not good..first have motor mounts checked, maybe the tranny mount or possibly if ur car has it is the driveshaft bearings...good luck on the oil leak...maybe tranny fluid..make sure if ur losing fluid that ur checking them incl. the tranny fluid...u might find ur leak first of all by rechecking the oil cap where it is supposed to be ...same with all fluid caps.

what is the transmision oil capacity?

try checking the fluid level in the gearbox,rodeo dont have a dipstick so u have to undo the plug on the side of the gearbox just like a manual gearbox.if the oil is really low i suggest doing a full service on the gearbox,change the oil and filter is ideal for better results.