Goodyear Auto Service Center Shoddy, expensive work. Kenner, Louisiana

i agree with the prev post, AND the rear brakes if they are drum are auto adjusting, there is a lever that pushes the adjuster when you go backwards and hit the brakes. Midas wanted $980 bucks for my wifes van brakes, I did them for $120 and 2 hours of my time. I need to go into the brake business

There is no doubt in my mind you were ripped off. $968 is enough to re-do your whole car. 
First of all, the noise you heard was probably your brakes wore down to the indicators which are meant to make noise so you know it is time to change your brakes.  Second of all I've never heard of anyone cleaning brakes, unless they replaced them. 
Do you know what you have to do to adjust rear brakes? (Assuming they are drum brakes, because disc brakes don't get adjusted.) There is an elongated hole in the back of the drum. You use a tool that looks like a flat head screwdriver with the head bent to turn a star adjuster inside. You turn the star until you can feel friction when you turn the wheel. (By the way that's not an instructional. ;) )
For $968 those "mechanics" made out like bandits. Your rotors: $30 apiece. Brake pads should be between $30 and $50. I could not find a kit to overhaul your caliper, but a whole new caliper is $40, so it wouldn't be anywhere near that. So essentially your parts cost at most $190.  That leaves $778 for labor. If the whole job took 3 hours, which I think is generous, that would mean they charged your nearly $260 an hour! 
I don't know if you can sue, but if it would made sense economically, you should. No shop charges $260 an hour. 
My suggestion is do your own mechanic work. Go to Sears or Lowe's and get a decent tool kit, with some wrenches, screw drivers, sockets and ratchets,  and maybe a hammer. Find out if the fasteners on your car are metric or standard, you'll avoid buying unneeded tools. Don't spend $500 on tools either, just get the basic stuff. Don't bother with Snap On or Matco; they aren't worth the price unless you are doing it for a living. You will need a jack and some jack-stands as well.
The next thing you need to do is look up EricTheCarGuy online. He has a website and a Youtube channel. He charges a few dollars for his full length videos, but they will be worth it for you. There are other people with repair videos too. I would stay away from the ones who make up their own  "redneck" way of repairing things.
One more thing, don't try to make up stuff when you fix your car. Do what the video says and do it the professional way. Don't add an extra gasket or put sealant on something because YOU think it needs it.  Watch the whole video first before beginning the repair and reference it during the repair. 
Go to the auto parts store and ask; they can give you advice. You go there and buy or order the parts you need, plus things like oil, brake cleaner, filters, and whatever else you need. Be warned though, in some stores the employees work off commission, so they will try to sell you the most expensive stuff and try to convince you it is necessary.
I think you'll save yourself a lot of money and have some fun in the process. Working on your car is really not hard at all once you get used to it.  
I can't end this post without saying this. When you take your tire off, when you put it back on make sure the lug nuts are on tight. I had a tire fall off once, and believe me, it was not fun. It was vibrating for a few days, but I had thought it was something else, and it was in the middle of the week, so I didn't have time to look at it, so I wound up in a ditch and had to have my truck brought home on a flatbed.