C.G.
Dear K.,
My first line of defense is to get to know the parents. I try to develop the relationship with the child/children simultaneously as any child welcome in my home must respect the boundaries and rules we live by. Yet, being loving and accepting with each individual is my goal. There can be a fair range of behavior differences if the relationship I've developed with the child allows them to respond to me. If you continue to make these efforts, you may be successful in allowing your children to play together. All children should be supervised closely to understand the dynamics that develop between them. What is said, what is acted out and the temperament dynamics are all important to monitor, guide and train in children to assure the properness in budding friendships.
With any behavioral issues with children yours are exposed to, you must put yours first. Small doses of time together can go a long way with you separating them when the neighbors don't respond to correction. Be sure to be honest with yourself if your own become the issue. There are times that not playing together becomes necessary and friendships cannot be forced.
Please remember, there are schooling issues, behavorial issues and there are parenting issues. Some children that are homeschooled are being educated that way precisely for the reason of behavioral issues. Many are not. Those issues would be present no matter where they received their education. The need may be more effectively met for that student and for the students they would be with in class with, for them to be at home. I would encourage you to view children in light of who they are rather than where they receive their education. You may find you have nothing in common with the parents and you may not click with them at all. If you do, you may just get past this and be able to live in harmony in your cul-de-sac.
Best of luck!