Are your children eligible for US citizenship?
laws at the USCIS website
If they're eligble for US citizenship, then you'd apply for that and shouldn't have any more difficulty enrolling them in a US school than you would a Canadian school if you moved.
You will need information from the Canadian manufacturer of your car, they call it a letter of compliance, in order to import it across the border. Your pets will need proof of rabies shots, and certificates of health, completed at least 30 days before you take them across the border.
You will also need to have lists of your personal and household goods that will be packed in the U-Haul. Nothing fancy, just number the boxes, write or type of lists of the contents, and have that ready, should the CBP ask for it. They usually don't inspect, but sometimes they do.