Demon,
It sounds like the cadets are responsible to arrange the carpooling from the crosstown school, While it looks like a van can be requested it seems it is not a guarantee. It would be a good idea to research the transportation options between the school. DC has a great transportation system, it just depends on the location of the stations as to how convenient it will be to travel between schools.
Make sure you son does a lot of research with both schools, find out how hard it is to schedule classes between the two schools.
There are a lot of cadets that attend crosstown programs, some are easier then others, all will have it's issues, it's doable but not always easy. Time management will be a must depending on the travel time between schools. Being at a cross town will have even more issues if your son decides to participate in things like Ranger Challenge or Color Guard, these will most likely be at the host school, meaning more trips back and forth. Once your son begins to have leadership positions he may find that he will have to make more then one trip a day to the host school.
Cadet ranking within the Battalion is very important, he will need to make sure he leaves himself enough time to be involved in many aspects of the Battailon, meaning more trips back and forth, working out the transportation will be very important. While GPA is the most important, accounting for 40% of the cadet's OML, the battalion review is worth roughly 26%, all of this will effect his chances of Active Duty as well as Branch Choice.
Just some things to think about.
