Transmission Vibrations When Cold

Ok, have a puzzling problem.

I have a 95 Skylark Custom with the 3.1. When the car is completely cool (like overnight) for the first five minutes or so until the car is warmed up and drove the car has a very distinct and very audible vibration to it.

The only point it occurs appears to be second gear. If you throttle up to about 20 - 30, let off the gas for a second and then reapply throttle the vibration occurs and will go away by 'punching it' for a quick second in which it appears to kick into the right gear.

The car also has the same type vibration/shudder when stopping between the last 10 mph or so and completey ceases when coming to a full stop.

Since I'm no transmission I asked a few people who said the transmission was just bad and others that mentioned some kind of switch, sensor or hardware that sticks and then once it is warmed up runs like a beauty. Other than this issue the car is pretty nice and worth even a moderatly priced repair.

Any ideas on what could be causing this?