Pacifica steering pulls to the left and car shakes

If the steering wheel is vibrationg it may be that the wheels need balancing. If the whole vehicle is shaking you need to check that wheel bols are properly tightened first. You might need to get steering/suspension checked .... before there is a bad fault developing

Have a front end suspension check done to eliminate any worm ball joints -shockies- worn suspension rubbers-- steering problems. If ok have a wheel alignment done and have the rear end aligned first as it affects the front alignment. The violent wobble is castor wobble and indicates negative castor possible from sagging suspension springs. The camber is out at that results in the car following every dip in the road. The camber has to work in conjunction with the toe-in measurement and if the 2 are not correct then you will have problems.

CHECK FOR A BROKEN BELT IN THE TIRE

Could the front control arms be worn out and letting the differential shift around ?

tires out of balance, completely blown out front end

If if the steering pulls every few seconds of driving
the car,why are you driving it at all?

Driving 60 mph knowing you have a steering problem
is,to be kind -foolish & iresponsibe

You need to have the enire front end checked out
for worn & damaged parts,as well as the steering
rack

Doubt it is the pump.

If the steering wheel starts to shake between 55-65 MPH then you need to balance the wheels. If it shakes when you press the brakes, your brake rotors are warped and need to be cut or replaced. If the steering wheel shakes at low speeds then it's possible one of your rims is bent or one of your tires is out of round. Leaving a car parked for a long time in snowy and icy roads will damage your tires, causing them to warp. Depending on which situation is causing your steering wheel to shake, have it looked at.

If the vehicle is FWD then you may have a CV outter joint going out and/or possibly a wheel bearing failure. I would have this checked out by a professional shop AS SOON AS POSSIBLE. It also could be causing the power steering alert to come on because it is detecting the vibration in the wheel arm for the steering. Good Luck, RAC

have you had a front end alignment

There could be numerous problems going wrong. Your car is rear wheel drive so it could very well be a bad wheel bearing. If it is extremely loose it can cause a shake in your steering wheel. You may want to check on the condition of your tires and rims especially the left front. A bad tire can cause a shake and pull. If you know how to use your car jack you can try jacking the vehicle up, and put both hands on your front wheel and move it manually to see if there is looseness. Most shops only charge about 1/2 hour to shake down the front end. BMW parts are expensive so be prepared!