I've been through this whole thing several times, and here's what I recommend.
1. Don't go anywhere or give them anything if your car is damaged enough to not pass a typical state inspection. This includes so much as a light out, or a cracked winshield. If they try to make you do otherwise, call your insurance company (if you have full coverage) and have them deal with the other party's insurance. That's what you pay them for.
2. Don't waste your time getting estimates. They should have a claims adjuster go to where your car needs to be repaired or your house and their claims adjuster should deal directly with the repair shop.
3. If they say you have to go to one of their "approved" shops, have them tow the car there after you look them up on BBB.org. If the company has a bad record for repairs go to your insurance company and make them negotiate another plan.
4. If you are not at fault, look at it this way, and stay firm. Insurance companies take advantage of "nice guys" if you don't set the bounderies straight from the beginning. This is not to say that you shouldn't be polite, just hold your ground on these important facts.
- Before the accident you had a car in good condition.
- Their insured changed your car's condition.
- At the end of your repairs, your car needs to be back to it's condition before the accident.
- You refuse to drive a car that isn't street safe until it is repaired, and the insurance company must not force you to do so, and must take the expense of moving the car if it not street safe.
- You need a working vehicle while your car is in repairs, comparable in size to what you had before the accident. For example, don't let them give you a Geo Metro if you were driving an Audi.
Hope this helps. I'm wishing you luck. I've been through this several times, and of course the first time I had to learn all this the hard way.