What is the purpose of the weekly 1/2 day in the classroom? What do they do?

I agree with aculady, you are finally out! Given you're experiences, I would stay out. Keep your freedom! lol

There are lots of curriculum choices and to be honest, as far as math goes, I don't think most public schools offer the best choices these days anyways. You could do Singapore math at home easily and IMO it is generally a better curriculum. Check out www.singaporemath.com
They have homeschooler/parent guides to help you.