Car Jerks Forward When Stopped/need Help Options

[Ih8Poserz]

This has been happening to me awhile now and I just recently found out it only happens when the A/C is on.

At low speeds the car will sometimes dip below the normal idle speed, shake/vibrate then rev itself back up to stay alive. Sometimes, it does not rev and the engine just dies and transmission (DCT) pops into neutral. Sometimes when going slow in parking lots, I'd release the gas and get on the brakes lightly and the RPM's would drop slightly and the car would jerk forward when revving the engine to stay running. Almost hit the curb at a parking lot because of this... car jerked forward as I was braking to a stop in a stall. When stopped at a light or stop sign the engine revs up past 1rpm then goes back down and revs again, then in rare cases the car would just shut off, causing me to turn it completely off and on again.

Basic problems: Inching forward in bumper to bumper traffic, A/C on, D mode, sport button off. Car vibrates at lower than normal RPM and dies. (Two times)
After coming to a stop at a stop sign, making a right turn at the intersection. Release the brake, apply light gas, car stutters and dies in the middle of the intersection with on coming traffic! (right turn on red)
Braking for a stop sign at the top of a hill. Car stutters, dies.
Numerous (and I mean a LOT of) other occasions where the car felt like it was going to stutter and die but the engine managed to save itself by revving the engine on it's own. All with A/C on.

Any advice on what this could be?