Ok. Lets see if we cant sort this out.
First things first, fix what is loose. Loose chassis and front end parts can cause all sorts of goofy issues, but often times, they will also accentuate other issues. You say the steering rack seems loose, but I would find it more likely that the inner tie rod is loose. There is a second ball and socket joint, similar to the outer tie rod. The inner is inside the bellows boot, and can be replaced. S chassis steering racks are relatively beefy for the weight of the car, and the stress put on them, I have yet to see one worn out. The rack lash does occasionally need to be adjusted. I would suggest trying to support the front wheels by the control arms, so as to load the suspension. Now shake it side to side. If the looseness is minimized, or gone entirely, then the rack lash is out of speck. This allows the rack piston to move up and down. If there is no change, loaded/unloaded, then most likely its the tie rod. You could also pull the clamp off the bellows and slide it down, you should be able to physically see what is loose when you shake it. The tie rod will move in/out, where as the rack piston would move up/down.
^^ Here you can see the rack outside the car. The drivers side has a bellows boot on it, and on the passenger side you can see the inner tie rod. You can also see the poly rack bushings.
Which side did you notice to be loose? Typically the steering rack itself will only show looseness on the left side, because the lash adjuster is at the base of the steering column. The right side has such a long run that it wont show looseness until things are really sloppy.
Another thing I would suggest checking, would be the front lower control arm bushings. If they are worn out, combined with the bad alignment, the front wheels could be walking in and out. It just takes a certain level of stress before it exhibits the problem, IE speed.
Then, you need to have the car aligned, and before it is aligned, make sure that a qualified tech checks over the suspension for any other loose parts. If an alignment is bad enough, it can also cause all sorts of issues, all though shaking isn't often one of them, unless its really really back.
Either way, fix the loose, get it straighened out, then you will have a better platform to diag the issue.