Car vibrates when turning right / accelerating

Have your CV joints checked.
I suspect that the one on the left axle is going to break very soon, based on the symptoms, but with 125k miles on the odometer, you should probably replace both CV joints if the left one proves to be bad.

Incidentally, it may be more cost-efficient to just replace the axles in their entirety, rather than attempting to replace just the CV joints on the axles.