You and your son can come to Canada to visit your partner. Usually Americans are given 6 months, and you can apply to extend this time about one month before it expires. So while you will be with your partner, living in his house, to the CIC and to any border agent you talk to, you are just visiting.
After you have lived with your partner for one year (which is possible as a visitor - many Americans have done so), he can sponsor you and your son for PR. If you get married, he can sponsor you right away (though it takes a while to get the application ready).
Some people have managed to get their child enrolled in school in Canada without having to pay international fees. If the stepparent goes to talk to the principal of any neighborhood school, they might let him enroll. Elementary schools seem more willing than high schools, and it is not a given that anyone will allow it.