Google Chiari malformation see a neurologist
Hm. How great has life been since they were out of school? Either something not so great was going on at school or they seem to feel they rule the roost and can make this decision on their own. So, I'd perhaps make 'at home' not so great in terms of comfort and luxuries (no tv, no electronics, etc.). good luck
Maybe there's things going on at school that needs to be talked about. Kids are very mean to each other at school. Have a discussion with your kids about it. Maybe even counseling will help.
How were the kids doing at school before the headaches? Are they in 6th. grade?
What did you do to get the headaches in control?
Are they afraid the school was causing the headaches? (molds, lighting, etc.)?