If you go active duty, you will not be working at VA. Navy is in need of peds/ob nurses, nurses overall. They got hospitals in many states (mostly in big cities) which serve both military and civilians, and yes military people also have children, sometimes critically ill, so probabbly yes you will have a chance to work in your specialty. . . .
There are a few ways Navy will help you and encourage you to go to grad school, CRNAs are needed and whichever way you will go or qualify for, the Navy will help you at least partially (or a full ride) to get there. Of course you will owe them some time for that but if you signed up you would expect it anyway, no??
Physical requirements are according to height, age and so on. . . my best advice for you is to go to www.navy.com
under nursing career and fill out you info. A recruiter will contact you and will answer all your questions. Had a wanderful experience with my signing up, recruiter and everyone else up till now. . .
Best of luck