That's a really difficult situation - but from a UK perspective, which might not be relevant, I'd be really reluctant to do what you suggest. Here missing school other than for illness is a big deal; state schools are assessed partly on their attendance records, and so really disapprove of parents taking children out. It may be different there, but here to take a child out regularly for non-illness reasons would put the child in an impossible situation at school.
I don't know what else you should do, though, with all the usual avenues blocked :-(
