Your intro says you are starting college in the fall. Here is my two cents:
1) You can put a price on education, and it is more expensive in time, money, and energy, to postpone school rather than get it done now. If you've started college, get through it. Give it a couple years and if it isn't for you, then join up. If it is for you, then finish school and get your degree. You'll be better for it and you'll learn a lot about self-discipline (staying in shape when everyone else wants to party, for example), scheduling, organizational management, and stress management because of it. You may also get some study abroad or other opportunities which will enhance your understanding of the world, and be more fun in general. The military will always be here, waiting patiently for willing volunteers.
2) If you're 18, you're a legal adult. Joining the military is one of the first adult decisions you'll get to make on your own. Don't let anyone take that first choice away from you. It's not your Mom or Sister or Dad enlisting, it is YOU.
3) You're not responsible for other peoples' reactions. You are responsible for keeping your word, doing your job well, and being a good man. If you forgo the military for college, do your best and strive to be the best. Same if you decide to enlist. Titles, accolades, and jobs will come and go, but your dignity and integrity are yours alone to protect.
Do yourself and your family justice by doing your research and coming to your own conclusions. For example, "Mom, Sis, I've talked to a lot of service members, former and current, and I know this experience will help me develop into a better man. I want to serve my country, maybe for a few years, maybe a career. I found that I might be a good fit for these jobs, plus I'll get valuable leadership training, etc." If they still are upset, then okay, it happens. You'll learn this sooner than most but it is okay for people to feel angry, upset, or sad. Those are normal human emotions and sometimes they have to run their course. You do what you know is right and do it well.