Hoosier
.....the car "wobbles" side to side when driving slowly through the parking lot at work.
It the tires are radials the tires are out of round unless they are built on nylon cord bias ply (1960 versions) and cold.
Lots of radial tires are out of round and some get that way as they age.
Random pulling left and right..... I am thinking of having tires rotated/rebalanced to see if anything changes.
Balance would not be the problem with pulling. If a tire had ply steer (a belt in the tire not vulcanized together) it would pull to only one side, not right and then left. Rotating tires (front to rear) would be worthwhile if you did it yourself just to see if anything changed.
Regarding the stiff steering, I would jack up the car and disconnect the outer tie rods and manually pivot each strut to the full right and left and determine if they both turn freely and listen for noises. Also check for any looseness in the struts or strut mounts.
I had a car that did what you described. It turned out the sub-frame was bent and I replaced several items but the car never did track correctly. Was the car in any accidents?
I worked in a tire and alignment shop for 20 years but never did frame measuring or straightening.