Without seeing your tires, no way to tell for sure via the internet. But if one of them measured 2/32, both tires on that axle should probably be replaced. It may be that shop's policy to not work on customer tires that are at their wear limit, as it poses a liability issue. If the customer gets a blow out which causes property damage or injury, the shop doesn't want to be in the position to explain why they released a car back to the customer they had worked on with a known safety problem. So as a business policy they don't do any work like rotating if the car has low tread tires. It's a lawyer thing, but it is also a safety thing.
I'd recommend once you get situated after your move to find a repair and maintenance shop recommended to you by a friend, co-worker, fellow church goer, fellow bar hopper, someone you have a trusted personal relationship with. Let the shop owner know who it was that recommended them. That gives you a little leverage in the customer/shop transaction, b/c they know if they don't treat you well, you will tell the other customer, and they may lose that business too. It's called collective bargaining ... lol ..
Tires are best purchased at your local tire specialty stores or Costco, if you are a member at your local Costco. Folks here seem to think Walmart is pretty good for buying tires too, but I've never used them myself. I usually use Costco. If you surf to the Tire Rack website (or many other tire related websites) they will list most of the tires currently being produced that fit on your car, and their prices. Best of luck.