I'm sure their will be some more elaborate explanations coming, but snapping is the wings stalling due to lack of air flow over them. useally from too much movement from the elevator.
Now when you say apply up elevator the plane rolls left. does it do anything else that seems squirly? like does it seem to porpoise during landings. (does the nose seem to want to bob up and down?) does the nose continue to drop when it rolls left if you hold elevator? does the plane do a fairly tight loop with only half elevator input?