Your mom doesn't know what she's talking about. She equates military service with ducking machine gun fire all day and returning home as an emotionless robot. That's not what the military is like at all.
As an army veteran, let me first congratulate you on your choices of Navy and Air Force. Both branches train their troops much better, and both will treat you with more respect--particularly the Air Force.
Whatever branch you eventually decide on, HAVE A PLAN. You can take college courses for free while in the military, and you have the GI Bill when you get out. If your plan involves making a full career of the military, that's fine--but you may well find that military life doesn't suit you. I'd recommend you choose a MOS that you can make a career out of on the outside, should you so choose. Communications and medical are good choices.
Make a plan, follow it, and change your plan if you need to. Don't be the person that does 20+ years in the military, gets out, and then sells used cars for a living because they didn't prepare themselves to do anything else. Having a plan will also make your decision a lot more palatable to your mom. Your mom sees your path now as military->go to war->die. When you can explain it as specialized job training, real-world experience, free college, more free college, and then your pick of civilian jobs in your chosen career, she might be a bit more understanding.
About being a woman in the military: civilians tend to think of the military as a nonstop parade of sexual harassment, assault, and rape. The military isn't without its problems, but for the most part, this is untrue. Reports of sexual harassment, etc. are taken VERY seriously by the military.