The symptoms for a bad PCS solenoid will vary but your symptoms sounds consistent with a flaky PCS solenoid. Get it scanned with a trans capable scanner or one that can read GM extended DTCs and see if a P1811 (max adapt, long shift) is stored which does not trigger the SES/CEL light. I recall the GM TSB addresses this specific DTC. Also, a bad PCS will affect TCC functions.
Since you are unfamiliar with the exact location of the PCS solenoid or replacement of it see the thread below posted at Buick Tips & Maintenance.
http://www.automotiveforums.com/vbul...38#post4994238
As you can see the PCS is located under the side cover assembly (driver's side) at the valve body. Not exactly a DIY job but it can be done DIY with the right tools and equipment to include lots of patience.
The engine and autotransaxle are dropped intact on the subframe assembly and then tilted which will facilitate removal of the side cover assembly. However, many other parts have to be disconnected or removed before that like the hubs and axle shafts, motor mounts, etc.