Jake,
As one of my (more bitter) NCOs put it, "women come and go, your career and the army will always be there".
If this girl is willing to draw a line in the sand over something she knows nothing about, think what other things she will try to control later on. If she is willing to try to control your life now, think what things will be like if and when you are married/kids etc. I would classify this as a "warning sign"
If you are going to join the CF, you need a grown woman who can stand on her own two feet and make decisions with you when you are home, without you when you are not, not one who tries to make them for you when you are around.
My 2 cents, give her the heave ho, training at various bases accross the country (and depending on trade/element) around the world later on is a blast if you are a single guy with no significant relationship or financial commitments. Many otherwise committed troops become so caught up in this atmosphere that they "forget" about significant others on the weekends. You'll meet plenty of, ahem "nice" girls, and won't be the one stuck with a dear John letter/phone call/e-mail to add stress to your training when she decides you've been away for too long.