When I accelerate hard, the car is all over the road.

 

Are your tires over inflated.
Why do you think this has to do with power steering?

 

Sounds like a torque steer issue.

Has it ever been wrecked? Checking the alignment numbers may give some insight.

Also check the lower control arm bushing. If there is a lot of movement the camber and caster can change on a hard acceleration.

 

dc98584 -In your first post just a couple days ago you posted "I've had my 07 HHR panel for 5 years now and love it! I'm now looking for ways to make it faster".

What has changed since then?

 

LCA bushings, inner and outer tie rods, intermediate shaft knuckles seizing, pothole adjusted the alignment for you! Torque steer all jump to my mind.