You only have the key cutters word that one fob is sending. I'm dubious that the key cutter knew what he was doing, so not going to take that as a definite.
Have you checked the battery holder connections to the PCB on either fob yet?
As for the 3rd, old, fob, that depends entirely on whether or not the dealer erased the old fobs from the car. The car allows up to 5 fobs to be programmed, so that might have left the old fob programmed. Impossible to say without plugging a Tech2 into the car.
The antenna is built into the ATWS ECU. Its part of the PCB. The antenna itself won't have failed (its passive), but if the surrounding electronics have, then it could stop the receiving side working. It would be a very rare fault, pretty much unheard of. Due to the varnish added to that PCB, diagnosis and repair is difficult, and if it was that that was faulty, I'd suggest a good 2nd hand replacement with 2 programmed key fobs and a carpass.
*HOWEVER*, I cannot stress enough, I believe your problem is with your existing fobs and/or the associated programming (esp if that key cutter plugged anything into the car's diags port)