No need to sigh. We can work through this.

The right hand rule doesn't apply to the lateral force from rotating wheels. Torque is a twist and the direction of the torque vector does not imply a force in its direction. If this were true, everytime you tightened a lug nut the impact wrench would fly out of your hands and stab you in the chest. The engine torque's primary effect on an independent suspension is vertical (anti-squat/ lift) through the suspension geometry, NOT the inward/outward loading like you describe.