This vibration comes from two possible sources;
Your road-wheel and tyre, tyres can move on the rim, due to braking and acceleration forces. Thus road-wheels need to be rebalanced periodically.
Your suspension system, components wear out, need adjustment, Elastomers (synthetic rubbers) harden and begin to break up etc.
Unless you are a trained mechanic, most of this stuff is best left for someone who is.
REPLACE THE STEERING DAMPNER SHOCK ASSEMBLY. THE SHUDDER IS COMING FROM THE FRONT TIRES & WHEN YOU TAP THE BRAKE, IT PUTS A 'DRAG' ON THE FRONT WHEELS AND STABILIZES THEM.
You may have a ball joint going out or your wheels are unbalanced
Wheels are out of balance
If the trye has gone out of round (an MOT failiure ) Yes the car will shudder when driving.
Unbalanced wheels or a bent track rod
Driving is on the left-hand side of the road with steering wheels on the right.
If the steering wheel turns, but the wheels do not on an automobile, the steering pin is defective. The steering pin connects the wheels to the action of the steering wheel. An automobile that has a steering pin malfunction should not be driven.
If it happens when you are driving fast (60-70 MPH) it could be that your wheels are out of alignment.
It is possible the power steering fluid is low,or the belt is loose.
Front wheel shudder could come from worn tires, bad brakes, or worn front end components. Check all of these to find the cause of the shudder.
COULD BE A NUMBER OF THINGS...YOUR POWER STEERING PUMP MAY BE BAD.
Sounds like your car might need either an alignment or the wheels have to be balanced.