Belts flapping when AC is on?

of course the condition of the pump is a player in all this. Daughters Durango is example. Early spring of 2015 she had expansion valve replaced and system recharged. It worked OK until Mid May this year. We know that expansion valve is full of crap again and we know where the crap is coming from. The pump is shot. Today when the clutch is energized the pump runs for a short time before that serpentine belt begins to slide and smoke.
New pump, new dryer, new valve, complete system flush, and hope the flush gets 99% of the crap out, very expensive gamble. Meanwhile, no a/c .