How can two brothers in different branches get assigned to the same base?

Sort of luck of the draw there, really. Pretty sure as far as the Air Force goes, if it isn't outlined in the regs, and there isn't a pressing need or family emergency, you're out of luck. Have you perused the AFI 36-2110? Another good option would be of course to talk to your immediate supervisor. Even if they don't know, they should help find answers.