Q: When I turn on the a/c, the car begins to shake then turn off.

Hello - your symptoms suggest that the idle air control valve is not kicking up the idle when the AC comes on (this should be automatic). It’s also possible that another component (leaky injector or worn spark plug/coil) is borderline, and the extra load added by the AC causes a misfire. I recommend a rough idle inspection performed by a mobile, professional mechanic, such as one from YourMechanic, who will come to your location, diagnose this problem, and give you an accurate assessment of damage and cost estimate for repairs.

It is likely that the A/C compressor pulley bearings or the unit internals are locking up because of a malfunction and since the air conditioning compressor is connected to the engine by the drive belt, the added load is causing the engine to have to use more power to run the compressor and causing the engine to stall at low engine speeds. Consider hiring an experienced technician like one from YourMechanic who can come out for a closer look at the car to offer a more personal diagnosis of your engine stalling concerns.