Your AC should have NOTHING to do with your barking system, as it is not tied into the vacuum of the engine. If your wheel shakes under braking, then you need to replace your rotors and pads.
maybe the car need to be linged up n check the power steering.
Tire out of balance, bent wheel, or if it vibrates only when braking you have a warped rotor.
You may need a wheel alignment, or you may need bushings.
During acceleration? I'm not sure. But when both idling and acceleration the engine's combustion can cause a lot of vibration in the steering wheel if you are in an older vehicle.
This can be a warped rotor or tire out of balance. If it only happens when braking it is a warped rotor.
All of the following causes mean you have a serious safety issue: Most comon is a bent brake rotor, but bent drums are also a suspect. Oil leaking onto the brakes can all cause this.
When the system is active this is normal due to the braking system being applied to a spinning wheel or a wheel that in under or over steering.
Out of alignment.......warped brake rotor......broken belt in a tire.....
Steering wheel and brake pedal.
bad front brakes.
well... there are many different causes for vibrations. The most common cause for steering wheel vibration at high speed is poor wheel alignment.
Go to a garage, and get the wheel balancing checked out on the front wheels.