Sell your vehicle before you move to the states and purchase a new one when you arrive to your new location. This will actually solve two problems. I can only speak on this subject based on what I have heard due to the fact that we don't have any school aged kids. Basically, the better the neighborhood, the better the school. The big difference between U.S. schools and Canadian schools is the range between good vs. bad schools.
Private schools are extremely popular in the U.S. and more so in some states than others.
Prices range from fairly expensive to VERY expensive. Each state has different laws when it comes to emissions and state inspections. California is the toughest and most expensive state to transport a vehicle into. Prices vary with a huge range. This way the dealership will do all of the running around and paperwork for you.