one thing you could try is file for CUSTODY, using her own claims that she has no car, no money etc... state that since she has no car she is unable to be the primary residential parent since she is not able to foster a continuing relationship and meet you for visits etc...
its a long shot, but might knock her into the shared thing a little easier
make sure when you go for your hearing, have evidence of her pay and her expenses or lack there of if you can, knowing the military.. its hard..or get her on the stand to question her about her expenses...
have a parenting plan ready to show to the judge, go for the max of week on and week off, let the judge see you are trying to share and be flexible... (have alternate 3 nights a week to just in case)
be calm, always say OUR CHILD, you'll do fine... let her refusal to share be its own evidence..
wait a week, then offer shared to her again, that way you have more evidence of your sharing, her not...
keep us posted..