I was a teacher in my former life, and I dealt with the homeschooling issue with my former stepson.
My opinion of homeschooling is similar to Shellcrusher's; I believe that children NEED socialization in order to understand how to function in a society where the focus isn't on them all the time. However, that sort of socialization doesn't necessarily have to occur in a school setting, but it means a lot of pressure on the homeschooling / unschooling parent to provide daily opportunities for socialization.
Generally, there are state or provincial guildelines you are required to adhere to, in terms of achieving certain skill sets. How and where you teach is entirely up to you. I'll tell you right away that it is A LOT of work, especially when your children move on to the secondary level, and you are required to provide them with challenge and complexity. Usually, in the first few years of teaching, a lot of time is spent researching, reading, designing lesson plans, trying out what works and what doesn't. When you are teaching your own children, you're sort of flying by the seat of your pants, unless of course you have set lesson plans and materials to begin with.
However, seeing as you probably won't have a class of 10, you can take your time and offer your children the individual attention they may need.
HOWEVER, some children may not respond well to having their parent instruct them...it's really up to you to assess.
Overall, the homeschooled kids I've met are generally way ahead of their public schooled peers, but they are completely lacking where working with their peers is concerned. This is a really important factor to consider, because at some point, your children will become young adults, and they may want to go back into the regular school system, where they will need those socialization skills.
Have you considered looking for an alternative school where there would be some freedom left to the student as to what they study?