This makes sense to me. You’re comfortable with your family so there’s no need to feel anxious or stressed. I’m the same with most of my family especially my nephews cause I often feel at peace with them. I enjoy their company a lot. I also stutter less if I’m around coworkers I truly enjoy hanging out with. I want to talk and I know they don’t judge me so often I don’t stutter that much with them. Anyone else or a new person I have to choose my words carefully. Though I realized if I’m able to have zen peace of mind I am able to get rid of most the anxiousness that triggers my stutter. I recommend doing yoga or even going to some meditation classes. Also join some support groups. You need exposure and also learn how to control your emotions. You won’t be cured but you’ll have some strong tools to help you get through school and life. Best of luck!