Check with the local school board. They should be able to guide you better on the process. However, if the parents are not holders of SP or PGWP, you may need to pay tuition fees (approximately around $15k/yr., depending on school) even if attending public schools. Plus, you will need a guardian for the minor child. If the minor do get a study permit, the parents cannot apply for work permit on the basis of the child’s SP.
FYI, local school boards may be on summer break for two weeks, starting this week (at least in Ontario they are).