yes and if it doesn't operate properly then u will not get the proper fluid to the clutch pack. i have dealt with these trans alot and the solenoid are known to fail. every time I have gotten any of those code it has always been the solenoid.
It may turn out to be that, but in my world of repairing/rebuilding all types of automatics across the board, we divide codes into performance codes and electrical circuit codes for diagnostic purposes,
Performance codes : meaning the computer didn't see the result of the command that it was expecting to see . Normally happens when the solenoid malfunctions mechanically, or a valve is stuck, or a problem with the clutch pack
Electrical circuit codes: the computer did not get the correct voltage/amp feedback it expected, or detected voltage when it wasn't supposed to be there, or no voltage when it was supposed to be there.
I realize the 5R110W is a somewhat different animal because the solenoids do the work of what you normally would expect other valves to do, but the fact that both of these clutch packs are tied in with the center support, makes me suspicious of a leak there, mainly because of the good reverse when cold, and shuddering/not holding good when the fluid warms and thins out. Most solenoid will act up cold, especially if there is contamination in the fluid, so solenoid D is doing opposite of what we would normally see if it is the cause of the shuddering in reverse.
Don't mind being wrong, and stuff like this is hard to diagnose without actually being there, and seeing PID's on the scanner to verify certain things. also can't replace in person seat of the pants drivability.