[Chop_E]

Thanks, I will try to get a mechanic to replace the bushings starting with the one you noted!

Mavis Discount Tire said that they couldn't balance the wheels until the rear right knuckle was replaced.
I am not sure how it is damaged, it is unclear.

Worn or damaged suspension should not prevent them from balancing the tires. Alignment is a different story but balance is completely independent of suspension and is actually done with the wheels off the car. Definitely find someone more competent.