this assumes a morris minor has a solid rear axle

the yoke (yolk) should go in half the length of the shaft on it, when the car is at ride height (or the car is held up by stands under the diff). this way it has room to slide in and out as the diff travels up and down

you probably have a balance issue with the new shaft, a good tail shaft guy can be hard to find. i have heard of many people having re-occurring issues using the same tail shaft guy, then taking it else where and getting a much better job

can you feel the vibration driving the car? if so it's either out of balance wheels, out of balance tail shaft, broken engine mount or gearbox/ engine jammed to or hard mounted to car

an obvious thing is if the steering wheel shakes when it vibrates, if so front wheels are out of balance if not then its one of the other things