The most common
location of a subclavian artery blockage is at the beginning of the blood vessel as it branches from the aorta. I am not sure why your Mother's Dr. is not recommending surgery at this time but I also do not know your Mother's medical history.
I do not know what is causing the fatigue and I would suggest you encourage your Mother to see her physician for a medical screening exam if this is a new sx for her.
I am sorry to hear of your Mother's problems and please know I am here to support you.