Well, that is probably the point I do not understand. You are a permanent resident, your son is in your care, there should be nothing stopping you from enrolling him. A study permit you only need for post secondary education, like college or university. I my opinion you have the right and obligation to send your son to school.
They say your son is not a PR holder.. how come? He cannot be a tourist, he cannot be anything else. Did you both come to Canada together? The whole thing I find is very complicated for nothing..