Your DS is covered under Tricare, specifically under the Tricare Prime option.
As you may know, Tricare is the military's version of an HMO so there are rules in play to that helps with cost containment.
The clinic at the USCGA is small so it is staffed to provide only primary care. Basically, the "direct care" it provides is what you can get from your local family medicine or internal medicine doctor. Almost all specialty care required by those at the USCGA is "purchased care" in that the military relies on the local medical network to provide when needed.
In the case of your DS, the same day surgery would be provided in the local network by a specialist in the local Tricare network.
The problem with your DS doing it at home is the provider (and facility) that will do the procedure will most likely not be in the New London, CT Tricare network (you don't happen to live in that area, do you?). Your DS's primary care manager (PCM) is at the clinic at the USCGA. He/she can refer to specialists only in the local network. If the PCM needs to refer to specialists outside of the local Tricare network, then special approval will be required (e.g. someone assigned to the USCGA with cancer needs to be seen at Memorial Sloan Kettering Cancer Center in NYC).
It is not the norm for a PCM to refer patients outside of the local network for non-emergency care like the kind your DS is facing. Put another way, if your DS was spending the summer at home (let's say Casper, WY) and he breaks his arm. The ER doctor thinks he needs to see an orthopedic surgeon. His PCM at the USCGA would have to write a referral for Tricare to approve that specialty care. In this case, it would be approved because your DS broke his arm and he needs (no question about it) to be seen by an orthopedic surgeon.
In the case you present, your DS's PCM can write a referral for him to be seen for the surgery near your home. However, Tricare probably won't approve it because the specialist is not in the Tricare network in the New London area AND there is no compelling reason for him to be seen at home other than for convenience.
You can try to get the procedure approved. Your DS will just need to ask his PCM at the clinic to write the referral for someone near your home. You have to make sure though that the specialist near your home is in the Tricare network. Again, probably won't be approved because it's more for convenience than for a clinical reason. Because his doctor doesn't think it's possible, then he may not be willing to write a referral to get the procedure authorized near your home anyway.
What procedure does he need done?