My relative's children are going into the fostercare system (most likely permanently). We presently homeschool our own children. What kind of invasiveness would be involved if we were to look into fostering these kids? Would my own children's homeschooling methods be questioned? What expectations from the state would be involved? Do you worry about having someone in your home making judgements about the things you say and the things your kids say?
I wanted to just get guardianship of them so I could make whatever choices I want (homeschool them without someone telling me how to do it and what to do), and not have the state involved, but that doesn't seem to be the way things are going.

It totally varies from state to state, but, we were homeschooling when we became foster parents, and it was a total non-issue. In fact, there are a few homeschooling foster parents in our area. It shouldn't matter at all.

Once they are in state custody, the state will remain involved until reunification or termination of parental rights occurs. Our experience fostering has been good so far- not too intrusive at all. But again, it all depends on your area. If homeschooling is legal where you live, it shouldn't be a problem, but you will need to get the caseworkers permission. They might be more willing to grant it if you use a charter school or something.

I hope it all works out for you. :)