Yes, they can apply in Canada. You'll need to be prepared to pay $15,000 per year in tuition for each child.
There is no visa specific visa for parents who are accompanying children on study permits. The most you can do is continue to apply for extensions to your visitor status and hope the extensions are approved. Note that you will not be able to work and won't qualify for health care coverage while here. Make sure you take out private insurance to cover medical emergencies.