2014 Jetta GLI, 2.0L inline 4 cylinder, 16v turbocharged/intercooled TSI. Engine goes into "stumbling mode" when AC/defrost is engaged. Will not right itself by disengaging the AC while engine is running. Must turn engine off and wait for "dieseling" to stop.
I will guess by "Stumbling", you mean it's bogging down and struggling to avoid stalling.
Check your AC pump is clicking on and off correctly. If the little pulley clutch is seized, it could click on and then not click off whilst under load from the auxiliary belt driven by the engine's crankshaft.
By dieseling, do you mean the correct term:
"Dieseling or engine run-on is a condition that can occur in spark-plug-ignited, gasoline powered internal combustion engines, whereby the engine keeps running for a short period after being turned off, due to the engine kicking back upon shutdown, drawing fuel through the carburetor, into the engine and igniting it without a spark.
Dieseling is so named because it is similar in effect to how diesel engines operate: by firing without a spark. The ignition source of a diesel engine is the heat generated by the compression of the air in the cylinder, rather than a spark as in gasoline engines. The dieseling phenomenon occurs not just because the compression ratio is sufficient to cause auto-ignition of the fuel, but also because a hot spot inside the cylinder (spark plug electrode, combustion-chamber/valve edge or even excess carbon) starts combustion. An automobile engine that is dieseling will typically sputter, then gradually stop. This is normally seen in carbureted engines with many miles on them."
Or do you mean just wait for the engine to stop turning over? An engine will continue to turn over after the ignition and injectors stop pumping fuel for about two-five rotations.
With the engine still running, the AC is turned on. The AC pulley for the Auxiliary belt is then engaged, allowing the clutch to make full contact and thus power the AC motor/pump. The bearings for the motor, however, may be heavily seized, causing excessive force to be used to make it rotate. This causes the engine's revolutions to slow down, either slightly or considerably to the point it stalls. The pump bearings are seized, and struggled to engage correctly under no load until it was needed. If it's under load (The belt spinning the pulley, thus spinning the bearings) then it'll find it very hard to disengage until it stops spinning.
It'll come on fine, but it'll struggle to turn off until the engine is off.
Good luck with getting this problem fixed, especially now it's starting to get warmer - I couldn't live without AC!