Ok, two things for ya.
First off, pop your hood, reach down into the engine bay to the steering rack and see if you can move it with your hand. I got $10 says you can. It'* two 18mm bolts from the back side of the craddle, jack the car, put a jack stand under it... go in with a wrench and you will see the two bolts behind the swaybar and sticking out from the rack that is mounted to the subframe. you go in from BEHIND the wheels, it is on the subframe below the firewall.
One of mine had backed allmost completely out, the other was not very tight. When turning or hitting hard bumps, I would get a bad clunk/thud, the whole rack was moving when the tire hit something.
Second thing to test for is your tie rod ends going out. Mine were also shot to crap and had to be replaced, helped a lot. you can test for this by jacking the car off the ground, even one side will do, and grabbing the wheel at 9oclock and 3oclock and doing a push pull motion, if it gives its tierods, the tire should be tight and not want to move, or, move the whole steering rack from your force. Mine moved up to 1/4 -1/2 inch when doing this, very bad.
If not the two above, I would say struts, but the whole moving back and fourth at low speeds sounds like the rack is loose.
Scope it out, let me know. mine had done this from 70,000 miles to the 110,000 it has now until I found it. Car drove fine, but had bad torque steer and walked when groves were in the road. Thankfully I found it and it was an easy fix.
report back. At least you can test the rack right away.. mine moved like it was just sitting in there. I discovered it by holding a video camera pointed at it in the engine bay and wigglin the steering wheel as I knew something wasn't right, when I watched the tape i could see the rack all like WEEEEEE YEEEEEHAAAWWW!!!! It was not good.
-= 2006 - Panasonic 8401U HU - 2 12"MTX Subs - MB QUART dB6500 6.5" components - MTX 2150x AMP - Kenwood 7202 AMP =- AMAZING 1.5L 109HP Manual 5.. :P