I had a 2002 Impala with the same problem, which acually became worse after a full transmission flush. In addition, there was a whirring sound coming from the left side of the vehicle in the vicinity of the transaxle. After doing some research I learned that it appears that this problem may be caused by a defective pressure control solenoid and GM has issued a TSB (#00-07-30-002B) for that issue. In my case, the harsh shifting from 1st to 2nd gear set codes that the transmission shop could read via a scanner. The GM 4T65 transaxle has a known problem with the planetary gearset wearing out early when driven under certain conditions. If you have not had a pan drop and filter change done I would recommend that service and use the latest version of Dexron, which is Dexron VI. You are at the point where fluid replacement should occur using the severe schedule. I strongly recommend that you avoid a full flush. I believe the flush I had done distributed dirt and metal particles throughout the transaxle exacerbating the issues I was having. I wish you the best of luck and that you can get some more life of your 4T65. We had our unit replaced at 84K miles due to the possibility of an internal failure.
