The buick might not be that expensive to fix, really. Your response to my questions has me thinking it's very likely a lower control arm bushing. That won't cost you a whole lot to fix if you have basic hand tools and the Taurtus is there to drive you around.
If you jack up the car (let the suspension hang) and remove the wheel. You might need a flashlight to see the bushing well, but if the rubber is torn or it has separated from the sleeve it will be easy to see.
To fix it? Not all that big a deal. You don't need to replace the whole arm. I'd recommend doing both sides at the same time to avoid introducing brake pull. You will need a wheel alignment afterwards. The bushing itself is pretty cheap and if the local auto parts store doesn't have a pair in stock, they can have it next-day. I can understand the labor cost of paying for a bushing replacement can sound bad, but you can probably do the job or at least most of the job yourself. I am assuming you have basic auto-service hand tools and do not have a lift or a press and probably no air compressor either. If you have any of those, it will make the job easier.
The first thing to do is to get the car jacked up and supported on stands or other safe equipment. Then you remove the wheels, loosen the axle nut, and take the arms out. Having a bungee cord to pull the knuckle away helps with removing the arm. With the arm out, compare the two arms. On one arm the bushing is pressed in from the opposite side compare to the other; make note of that. Use a file, center punch, or similar tool to mark the control arm indicating the clock position of the old bushing. Do not use paint or Sharpie to mark as your marks may disappear before you need them. This is important because installing the new bushing in the wrong clock position will change handling characteristics.
Now, if you're okay with spending a little more money take the arms and the bushings to the local garage to have the bushings pressed in. Remind them to clock the bushings correctly and agree on a price before you let them do the work. About a half hour at the standard shop labor rate is fair. A dozen bagels along with some cream cheese and butter or maybe some coffee "for the guys" just might buy a little extra care and attention when the job is done. It's your call if you want to spend a couple of extra dollars in hopes of getting better work. When the pressing is done, check that the bushings are pressed from the correct side and aligned with your marks before you leave. If they're not, well, somebody owes you new (not the same ones) bushing put in the right way.
If you're prepared to do it yourself that shouldn't be too big a deal either. Without a press to push the bushings in and a pneumatic chisel to remove the old ones plan on maybe an hour and a half instead of the half hour the shop might need. You also might need to make a trip out to the local plumbing supply house or home improvement store for a tool, but a little planning ahead can make that unnecessary.
If the rubber's separated from the sleeve removal is as simple as nicking an edge and peeling the sleeve out with a vise-grip in the manner of opening a canned ham. If not, well, you could use the awesome power of fire to remove the rubber then do it that way, but I wouldn't as it's nasty and stinky. It's more pleasant (but more work) to use a narrow sharp chisel and a hand sledge (hammer with a heavy head, hard face, and short handle) to remove the complete bushing from the arm. You'll need to mount the arm securely in a vise or whatever you can work out as a suitable substitute if you haven't got a vise.
To install the new bushing isn't too difficult. Before you begin you'll do well to deburr the hole and consider lubing either the hole or the bushing for ease of installation. You could maybe start a new thread to discuss at length the relative merits of thread locker/grease/antifreeze/whatever, as suitable lubricants. Without a press you're going to be pounding the bushing in with a hammer, maybe the hand sledge I mentioned earlier. Ideally you want to use a socket that can butt against the outer sleeve of the bushing while missing the rubber completely. Use this socket as a drift and hammer at the center of the socket. A suitable peice of pipe will also work, but you'll be tapping around the circumference of the pipe as you go constantly correcting for the bushing going in slightly cocked. The straighter you drive the bushing in, the less force you need to apply. If you used lube it might feel good to stake the bushing into place once it's in, but isn't necessary
With the bushings installed in the arms, whether by you or by a shop, it's time to put the arms back in the car, tighten the CV axle nuts, put the wheels on, then drop it down and take it for a wheel alignment. These bushings do not bear the load of vehicle weight and do not require any settling time before the alignment.