Q: When I turn my car on it bogs down off and on but when I turn my ac on it will keep doing it worse and then the car starts shaking

There are a number of things that may cause the engine to bog down as you describe. The reason this appears to be worse when the AC is on is that the AC compressor requires a bit more power from the motor to turn it when the AC is on. It is likely that the problem exists outside of the AC, meaning that the AC is not causing the problem.

A clogged or failing catalytic converter can cause the vehicle to have poor fuel economy. As you may already know, the catalytic converter converts toxic exhaust gases into less harmful pollutants that are suitable to be expelled into the atmosphere. When this is clogged, this causes these gases to be backed up into the exhaust system not allowing the engine to breathe properly. When this happens, the engine is forced to work much harder to expel these gases. This often results in the engine bogging down, hesitating, shaking and causing very poor fuel economy. In cases where there is too much fuel being provided (i.e. a leaking fuel injector), this may cause the engine to bog down and produce a fuel smell and occasionally, emit a bit of black smoke from the exhaust or cause problems with starting.

Shaking or vibration may be caused by many different things such as faulty spark plugs, poor fuel pressure or misfires. Other things such as a faulty idle air control valve may cause the engine idle to drop below the normal idling RPM which may also cause the motor to shake or vibrate more than normal. This creates a loss of power that resonates throughout the motor additionally causing other problems with ignition and fuel timing. Anytime a misfire is caused, this causes an imbalance in the motor which will cause the motor to shake or vibrate. Other issues that may cause this type of shaking or vibration might be broken engine mounts or potentially tires that are out of balance or worn improperly. Engine mounts are generally rubber mounted braces that hold the engine in place to the chassis of the car. When these break or become weak or faulty, this may cause the engine to vibrate heavily. When tires are out of balance, as the speed of the vehicle increases, the vibration will become much more noticeable and pronounced. I would suggest having an expert from YourMechanic come to your location to diagnose and inspect your vehicle using a scanning tool which will more accurately indicate what specifically may be causing this.