Join all of your local homeschool groups and start becoming active immediately. I am only a member of one, because it works well for us and offers way more than we can ever participate in, but here is a list of the things that it offers:
-weekly park, beach or pool days
- family potlucks every couple of months (some with themes, like multicultural or science fair, some not)
- boys clubs, girls clubs, 6 & under clubs, teen groups, etc., that meet weekly, monthly or somewhere in between for social activities, field trips, etc.0
- 4H, book study groups, Roots & Shoots, chess club, craft club, drama club
- various year long science classes you can sign up for, where a group of homeschoolers hire a science teacher to teach an ongoing class like chemistry or biology to highschool aged kids
- field trips galore, usually 2-4 a month
- events like curriculum nights, where people bring their current and older curriculums to show them off to others, so every can chat and get a hands on view about what has worked for them best, and where people can sell used materials to each other
- and much more
There are endless amounts of curriculum choices, even secular ones (or mostly secular), things like K-12, Calvert, and all sorts of piece meal items so your son can customize his education according to where he is in each subject.
9 years old is probably old enough to just sit at the edge of the gym with a book or a hand-held game and hang out while you work out. Or once you join that homeschool group and start becoming friends with others, perhaps you could make a gym buddy, someone who will take turns with you, watching each other's children while you each work out. Or just switch your work out schedule up a bit and work out at a different time of day when your partner or a friend can watch your child for an hour.
Homeschooling siblings who are 4 years apart isn't hard at all. First of all, even if you go a curriculum-based route, remember that with an hour or two a day, your child will most likely be learning way more than their age-based peers in public or private school. If you just join some homeschool groups, become really involved, get to know other homeschoolers and see their children and ask about the wide variety of routines everyone has, I swear you will feel so relieved to know that it isn't as hard as it might seem and that children are sponges and once they are ready, everything can be a learning experience.
Social experiences are well, the easiest and best thing about homeschooling. My children have oodles of homeschooled friends, see them frequently, are always making new ones, are involved in tons of music classes, art, sport, science, history and various other classes that come up throughout the year, every year, and they love to join in on as many as they can manage, and we are unschoolers. I feel bad for kids who are confined in schools, rarely are allowed to speak freely and even if they do, it is in 10 minute snippets, hardly any sort of bastion of getting to deeply know and interact with others. I am always so happy when my children get to play and interact with others for hours at a time, regularly, and really bond with them at such a much deeper and meaningful level, at the same time enjoying plenty of lighter moments with others, too.
Of course, we don't lock them in closets and we take them with us when we go to festivals, on field trips, to grocery and drug stores, browse for furniture or clothing, go to libraries and book stores and coffee shops and restaurants, so I may be biased, but I get the feeling they have plenty of experience with social interaction!
BTW, if you talk to your gym, I imagine it would be foolish of them to not change their policies regarding older children (surely your son is not the only homeschooled kid in your town) and allow your son in the children's area for an hour a few times a week. I imagine they would be perfectly happy for the extra money? And you could sell it to them, by saying that you know of plenty of homeschooled parents who would be extremely eager to join a gym with such a fantastic service.