First--I want to tell you to just relax...:) I would go onto Yahoo groups! and find a local home school support group or co-op--this will help you and your child soooo much! Because we all have been there.
K12 is "school at home"--actual home schooling is simpler, less complicated and--IMO--a lot more fun for everyone! The stress is not as intense and you find that have so much more has been learned than you ever thought possible.
As for socialization: http://jacksonvillehomeschoolkids.yolasite.com/socializat...
this is a thesis paper on that very subject. You will not find even one study that has been done that will state that public or private school is better in any area than home education. These are facts. Educationally, schools such as Yale, Harvard and Brown have specific slots available to ONLY home schoolers because they want them that badly! I know--I called them myself.
We have PE, Art Days, Field trips galore, Science Clubs, Book Clubs, Park and Beach Days, special shows only for HSers and take a look around town--Museums, Nature preserves and more have days ONLY for home schooled children...Including Disney!!
As for jealousy--if you have offered this option to them, and they do not take it, then it's a lesson they need to learn. You have opened the door--just don't close it too fast and let them make a decision on their own. Explain what you are doing and explain that because it's one on one--that no--your 8 year old is NOT going to have as much work, or spend as much time as they do at school. The average HSer spends an official 3 days a week two hours a day on book work and such. Most HSers have their education supplemented by home school groups, real life situations and life itself.
In no other environment, but school, will you have one "leader" telling you what to do while you are around people the same age as you. So why let them grow up that way? Let them grow up to already being accustomed to being around varying ages, that will help your child and you along the way.
Your other two children have had the door opened..They need to choose to walk through it or not. But you can not let one child suffer because the other two feel put off by it. AND this is not uncommon! I have members in my own group who homeschool, but have other kids in public school.
This is not for everyone--but for those who chose this route, I will always advise them not to do it alone.