What term describes the rear suspension component that supports load while allowing side-to-side movement?

The term that describes the rear suspension component which supports load while allowing side-to-side movement is the rear leaf spring. Leaf springs are designed to support the weight of the vehicle while providing flexibility, which allows for lateral movement as the wheels encounter uneven surfaces. The leaf spring's layered structure provides both strength and the ability to absorb shocks, making it effective in maintaining ride quality and vehicle stability.

In a typical vehicle suspension system, the rear leaf spring serves a dual purpose; it supports the vehicle body and maintains its height while also allowing for some independent movement of the wheels. This flexibility is crucial during cornering and dynamic driving situations where the wheels on either side may need to move independently to maintain contact with the road surface.

Other components, such as control arms, primarily manage the wheel's vertical motion and alignment, shock absorbers control the oscillation of the springs but do not support the load directly, and axles transfer power and torque to the wheels rather than directly supporting the vehicle's weight in terms of suspension dynamics. Therefore, the rear leaf spring is specifically designed to meet the criteria outlined in the question, making it the correct choice.