If I want to enlist in the Navy, should I tell my family?

I think you should bring it up now. You don't have to say you're 100% gonna join, but express it as an interest. The more they're educated about your decision, the larger the likelihood that they'll end up supporting you. Most of my family and friends tried to talk me out of joining the military for 3 years before I finally did it. They also had me talk to my uncle who was in the army, and because he realized i'd done my research and had a plan he approved and it made my mom a lot more comfortable with the idea. Now she brags about me being in the Navy alllll the time. She knows I'm happy and made the right choice for ME.

I do not feel this is a good Idea.

True, you will be 18, and free to enlist yourself as an adult, but I would talk and be frank with my parents. Educate them about it, take them to the recruiter with you.

the more they know, the more they can be on your side.

Better that they know, cuz when you don't come home for four years they'll get a little suspicious

Sure, why not.