Dennis......I see no issue with what you did. I would rather drive on a flat tire versus the damage that CAN be done while trying to flatbed tow the coach. A small coach is fine, but a 45' is much more difficult to get on a flatbed without tearing up the front end fiberglass.
I would let the adjuster do their thing and see if they still deny the additional work. If they do, I would ask them about their procedure for you to challenge their decision, politely saying.....do I challenge Geico by a complaint to the State insurance commissioner, or would I just file a small claims case for the additional damage. Again, you just want to intimate these ideas, not threaten. If you get nowhere, document everything and take them to small claims. They won't show and you'll win by default.
I would also ask the repair shop to provide a document that describes that the damage not covered by Geico was actually caused by the blowout. Small claims will ask for some sort of expert to prove your case. A document from the repair company should be sufficient.