young kids and school

The question that I have is...
I am a Canadian hoping to either obtain dual citizenship or stay Canadian but have a house in the US. I have three school aged children. What I have read is that I am allowed to be in the United States for up to six months and then back to Canada for the other 6 months; however, if the children were to go to school in the States they would be in school for 10 months out of the year. What would be the best route to go?

You and your children would be entering US as tourists -- nothing you have posted would indicate that you can get any other status. Tourist children are generally barred from attending school in US.

You can only visit US.