Sounds like the idle is set too low. That steering wheel shake is probably from the engine on the verge of quitting because it's idling too slowly with the air on and the car in gear. There might also be a 'fast idle' solenoid associated with air con that is not being activated when the air con is turned on.
Turning the air off and trying both drive and reverse will confirm, at least to some extent, that the idle is only too slow when the aircon is on, that is if the jerking steering wheel behavior doesn't occur.
Then it's down to a simple idle adjustment, or at worst a look at a fast idle solenoid that may need replacing. With or without the solenoid, adjusting the idle a little faster should make this go away.
There are several causes of this but the most common we call a head shake. This is when the tires shake side to side, the cure is to insure the steering is tight and you add one or two hydraulic steering dampers.
tune-up time...read up on basic idle diagnosis in the manual.. everyone should have a manual for their vehicle, and the library should have a professional shop manual available in the REFERENCE section...make copies of the right sections...good luck :)
Worn steering and/or suspension components. Don't drive that fast until you can have the problem repaired, and try to NOT drive very far.
Check into a new steering dampner, it's a common cause for shake at speed in a Jeep, but it could also be alignment or balance.
Track bar joints worn out.
No it is not common for dogs with beagle in them to shake violently. Some reason why dogs shake violently are seizures, and poisoning. If you dog begins shaking violently, it is best to take it to a qualified veterinarian who can figure out what is going on.
Tire out of balance, bent wheel, worn steering or suspension parts, broken motor mount, bent drive shaft on RWD vehicle, are just a few things that can cause this.
have you tried to get your wheel realigned
1. out of balance wheels 2. misaligned front end 3. worn out steering dampner.
It's possible, but unlikely. However it will shake violently at certain speeds and may damage steering gear and tie rods.
Tire out of balance, bent wheel, drive shaft bent, loose or worn steering parts.
Loose/worn steering components. Especially the steering stabilizer shock and the trac bar.