As a mom, I can tell you that watching your child do something that might put them in harm’s way is very difficult. In addition, when a young person leaves for military service, they are basically “gone from the nest”. There are no long summer breaks when the kid will once again be hanging around the house. It will feel to her as if you do not need her anymore, and after all of these years of having her life pretty much revolve around being a mom, that is very difficult. That part of her life and your time with your parents will be over. This will never be an easy thing for most moms.
That being said, it is the most natural thing in the world for you to want to be independent and become the adult she has raised you to be. Continue showing her that you are responsible and remain driven in your goals and she will over time see that you are serious about this.
Again, she may never utter words that seem supportive (because she will miss you like her right arm is missing) but she will be proud of you at the same time.
Best of luck.