Worn top suspension bearing (McPherson strut).

Worn tie rod bushes.

Worn engine mountings..

You garage appear incompetent. Change them and get someone competent to investigate.

I have had just a single front spring changed on my car in the past. It didn't make any difference to how the car handled or drove whatsoever. I was told by my garage that it was only necessary to change one spring, the broken one. This advice proved to be correct.

As most cars travel one up most of the time i.e.occupied only by the driver, it is common sense to assume that if the o.s.f. spring has broken or become weak it will have been under more stress than the passenger's side. Therefore starting with a level playing field of having two new springs will prevent any problems occurring from replacing only one. Any slight difference in ride height from each side will alter the steering geometry and can cause problems such as the op has experienced. If there is no apparent wear on any of the steering or suspension components and in the absence of accident damage then changing the other spring seems eminently sensible to me, so unless somebody somehow managed to brake a front spring when collecting a new car from the showroom they should always be replaced in pairs.