Years ago in Popular Mechanics magazine there was a serial called Gus Wilson's Model Garage.
One of his customers had a car that kept stalling out... It ran fine for his wife but stalled when he drove it and made either a left or a right turn (forget which too many years, I mean I read that mag in High School).
His wife was convinced it was because he was overweight and he needed to loose weight.
Turns out... She was sortta right.
his KEY ring was overweight.. When Gus took the ignition key off the ring the problem disappeared.
(I might add the last bunch of Ignition locks I've looked at (Locking wheel types) likely that would not happen, they work differently).
I agree with Gary, Suspect 1 is side to side weight load.. Get ye to a scale
Suspect 2 is a broken suspension part (Spring, air bag, whatever)