Last one... promise! The most special memories for me are probably the everyday ones of just being together as a family. The older siblings snuggling the new baby in the morning because they aren't rushing anywhere. The 8 year old helping the 6 year old with spelling very authoritatively and making atrocious mistakes while the 11 year old and I have tears rolling down our cheeks from suppressed laughter.
Again, homeschool doesn't have a monopoly on these moments. I think we just plain spend more time together, which helps.
It does seem to be more common among homeschoolers to have kids really play with and appreciate all ages. There's no eye-rolling about spending time with the younger ones.
By the way, you asked for "special" moments and I took the positive spin on that word. But homeschooling is definitely not all roses and there are plenty of especially tough and messy memories I could have shared as well!