That's simply the way it works as outlined by jwzimm. They'll handle everything and you'll get your deductible back once they collect.
As far as the gas and time, they'll simply tell you to use their local preferred shops then, if you want to use a shop of your own that's your perogative but also your time and effort in geting there and back.
You mentioned custom wheels, did you have them declared and can prove the value? All they legally have to do is return the vehicle to the declared state so if you do a bunch of custom mods, do not declare them to your insurance you will be out of luck and will need to go after the other party for the difference.
As far as who was at fault, the police report will be all you need, was the other driver cited? If so even more in your favor.
No need to stress, good thing you both were insured, that's becoming rare these days.