Spiker,
The Auto Pilot controls the aircraft through the trim settings. What you are describing sounds like you stick is somehow altering the trim setting. Try this off-line. Pick your favorite aircraft and launch to the runway. Note the trim setting. Move the stick and see if the trim indicators also move. I fly with manual trim and have trim mapped to a hat switch on the stick. Assuming you also have the trim function mapped to something on the stick, a broken wire, loose connection, or short could activate the trim circuits as you move the stick. I recently had a broken wire in my redder pedals that would cause the left toe brake to fully activate when I deflected the rudder bare more than 75% to the right. You could have a broken trim circuit wire that gets pulled apart when you move the stick to a certain position causing the trim settings to change.
GL
MachNix