We are much closer as a family than most PS kids. We have a great time together and when I meet PS families they are always a little amazed that my kids seem to have bypassed the "sullen, rebellious age" they are told is so normal with their kids. From my observations that is a byproduct of the school system.
Homeschooling has its drawbacks as well as its advantages. Despite what the liberal media would have you believe, huge amounts of money are poured into PS and that is sometimes hard for a HS parent to compete with. For instance, I have always regreted that I never had a really great microscope for them to use like I had in HS or other science and art supplies that I can't afford. But the trade off is FAR worth it.
As far as a prom or sports goes, depending on your area, you can find hs'ers organized to offer such things. You can get class rings and other stuff. The kids in my hs group have a group ethic where they actually feel like a school as far as socialization goes. They skate together, have beach day, graduation ceremonies, etc. Today my son is going to a language class with his friends. They just aren't herded together without parental supervision for 8 hours a day.
Wow, this is a long post but I hope it tells you some interesting things about homeschooling. If you have the commitment there is nothing more rewarding. It is like you actually have your children to ENJOY them, and don't have to ship them off all day into the care of others. We have a great old time.
Now, the oldest is 9, the middle is 7, and her youngest will be starting schooling next year. The two in school now can carry on complex conversations in a broad range of subjects with most adults. That's because they have learned at their own pace, not held back by slower students, and their curiosity can be explored freely, not limited by a bell ringing every 50 minutes. They learn to think creatively and with complexity and perspective.
I swear, talking with the oldest one makes me feel like I'm talking to George Will.
Obviously, now the family has seen the wisdom of homeschooling.