It's refreshing to see that the Air Force/Navy debate is still going strong (24 years in AF). As far as who will control this space force, it always comes down to politics (in other words, who has the bigger stick). For a long time, the Air Force has always been the second banana since it is the newer of the services. But it is possible for aircraft to stay airborne for quite a long time and they have. Most of the air force planes are refuelable and that is used to keep them airborne for quite a long time. I would definitely suggest a combined force instead of a single entity. That way both sides would be appeased and make it easier for the OP to just concentrate on writing a great story.