I have the blessing of being the youngest in my family, so I've been able to watch my older siblings navigate this whole extracurricular activities thing. Observing them and reading "The Socialization Trap" by Rick Boyer has lead my dh and I to the conclusion to simply homeschool and put ourselves in charge of extracurricular type things for our kids - in other words, not to have our dc in any extracurricular groups.
Before coming to this conclusion, we had our ds in softball, which was fun at first, but quickly became a deterrent to doing what we "really wanted to do", which was hang out as a family. They had games twice a week, and while my ds enjoyed it at first, he didn't like missing time with dad at nights, since that's his only time to spend with him. He also wanted to just play outside more, so the next year when the softball team would be traveling to other towns, the season would be much longer, and our middle ds would start playing on a different team with different nights and places to play than our older ds, we realized we'd all be split up and we chose not to continue. It wasn't easy at first, my oldest liked baseball and still does. However, we did kick it off with the purchase of a small used 3-wheeler for him, which helped immensely.
Our current vision is to give our dc lots of time to be creative, play imaginatively, be with their siblings, hang out with their dad when he's home, and invest time and money in doing things as a family. Our average day looks like this...homeschool from 8:15 AM -12:30 PM. As for the rest of the day, I'll copy a previous post for that part:
We stay home during the week, so our afternoons look like this...
1-2 PM Outdoor playtime (ride 3-wheelers, scooters, baseball, rake leaves, sidewalk chalk, garden, sand box, bikes, sledding, etc.); if poor weather than they do an indoor exercise video
2-3 PM Creative time (playdough, origami, perler beads, art time, erector sets, lego creations, make cards, puzzles, write a story - anything with a product)
3-4 or 4:30 PM Playtime with toys
4-4:30 or 5:00 Educational video (Magic School Bus, Zooboomafoo, Liberty's Kids, Bee the Creature, Reading Rainbow, etc.)
5-5:30 Quiet time in rooms (read books, audio books)
5:30-6:00 or 6:30 play board games or educational computer time
For extracurricular type things - here are some things we've done this past year:
3 wheeler riding, fishing/camping with dad, deer hunting, above ground pool in our yard (on clearance from Walmart), went to a Twins baseball game in Minneapolis, family vacation with my sister's family and my parents to Branson, MO; water balloon fight with the cousins at our house, did a mystery supper with extended family, played Bunco with extended family, b-day parties for each of the boys at our house with extended family, movie nights, sledding (behind 3 wheelers too), trapping with my dh (NOT my thing), family board game nights, completing large puzzles together, fourth of July party with fireworks at our house, going on walks/biking together, inviting cousins (which we consider their friends) over to play and letting each one pick 1 thing to do each for 30 minutes (great fun), getting an activity table for Christmas (ping pong, pool, air hockey, fooseball), etc. New Year's Eve fondue as a family, picnics outside and inside, working for a farmer pulling fence (my dh did this with the boys), private swimming lessons for a month, making Christmas cookies with the cousins, etc.
These are all things that have been added gradually, as funds allow and time allows. We don't do video games, Xbox or Wii, nor spend money on outside the family extracurricular events, so we put our money into things that can be used a long time (i.e. 3 wheelers, a pool, activity table, etc. and also toward special one time things like once a year vacations and one time event things. We love our life, and so do our dc. Anyway, I know this is a different perspective and that it will not work for everyone - nor do I believe it is the only right way to go about doing things - but it is working beautifully for us. I can easily finish school, we are a very close family, and we spend our time together doing things we love.
This year I've also started adding "dates out" with individual sons. I take one of them to town for hot chocolate and play board games there (the little place in town has games there) and we go to the dollar store for them to buy one gift for each boy. They practice getting doors for me and using good manners, and we just enjoy hanging out and talking alone. It's great fun! This past "date" my middle ds and I went Christmas shopping, making a list of gifts just for him. He felt so special and loved it. My oldest is asking when our next date will be anxiously...

I usually do this once a month or every other week, so they have to wait awhile for it. I think it makes it more special.
One last thing we've learned about approaching activities in a family manner - it is best to pick things WE as parents like and go from there. When we are enthused, they are enthused, and we all enjoy ourselves. For example, I love hot chocolate, shopping, and being treated like a lady

, so that's what we did last time. My dh loves to hunt, fish, and ride 3 wheelers, so they enjoy that together too. I don't like going to the public pool, so putting one in our backyard was a huge relief. I love to cook, so fonduing, cooking for parties, etc. is great fun for me as well as for the boys. Both my dh and I like board games and are pretty competitive at ping pong

, so that was fun too. We enjoy vacationing with my family and like watching baseball - so that's where those came in. I love music concerts, so I'll probably take my oldest to a Christian concert soon. Anyway, I think if you begin with what you enjoy as parents, the dc will be blended into that, traditions that last will be started, and everyone will be excited to be together enjoying life as a family. At least, that's our goal!
In Christ,
Julie