Also, in our state of New York, homeschooled children are only eligible for a GED diploma. My daughter's dream is to study business administration at NYU. I've told her that this would still be possible if she was homeschooled through twelfth grade. Can you offer any more advice?
As a homeschooling parent of two very social girls, one a preteen, I find there are more social activities available to us than we are able to attend. My family initiated several of these activities with little or no organizing. For instance, we love to ice skate. I emailed several local homeschool groups a message that Friday mornings at our local arena would be homeschool skate day. Within a few weeks, we had a very nice turnout of homeschoolers.
On another occasion, several of the moms of teens complained there weren't enough teen activities. With the guidance of another dedicated mom, we put together a teen group that meets on a regular basis for socializing and group activities (laser tag, movie night, game night, etc.). The first few get-togethers were a bit awkward as the kids got to know each other, but now friendships have formed and it is quite successful. In fact, for the second year, they've had a homeschool prom with almost 150 kids attending. For our family, the extra work of coordinating or assisting teen activities is far more desirable than participation in what passes for "socializing" in many public schools today.
As for the sports, perhaps your son can participate with a community-based team. My daughter is active in soccer and tennis. There are also basketball, softball, swim, and hockey teams, to name a few. Unless the child is truly gifted athletically, community team sports fill that need for competitive group activities.
As far as a diploma, have you considered a correspondence or online diploma for your kids? There are several private schools that will provide a diploma that is acceptable to most, if not all, colleges. Try Clonlara School, Oak Meadow School, or Calvert School.
Lastly, I suggest you read Homeschooling: The Teen Years: Your Complete Guide to Successfully Homeschooling the 13- to 18- Year Old and And What about College? How Homeschooling Leads to Admissions to the Best Colleges and Universities, both by Cafi Cohen.