2002 Buick Regal transmission

2002 Buick Regal mileage: 40,000 The trans. Initially had a delay when placed in drive when cold and then would grab. After warm up, the lag was gone and operated ok. A year later it still has lag when cold but operates ok until it gets completely warmed up (30 min or more) and then if seems to stumble in drive and low ranges (engage/disengage?) 2 or 3X from a standing start. This confuses the computer mixture control system so the car stumbles and or cackles until it catches up with itself. After revving the engine a few times and letting it come back to idle and placed into drive, it will sometimes not stumble. Holding brake and accelerating gently causes the car to pulsate arithmetically. It will shift and downshift ok once past the stumble. It doesn't happen in reverse. What in the transmission is causing this condition?