Susie, I know you asked SBG, but I have an answer too.
As quiltingshorttimer mentioned just above, every public school is required to allow homeschool students to attend specific classes, like the sciences that need a lab you mentioned. As for music, you can always hire a tutor. My Dad is a music teacher and would often get homeschool kids going to him for private lessons for years. He really enjoyed teaching them and they always loved their weekly lessons. That's how my Dh learned Greek and Latin, by private tutoring.
Home education isn't a "handicap" or a stunting of children's knowledge.
I'm sorry your Catholic education left a bad taste in your mouth for Catholic religion. But please remember that just because one school was operated like that doesn't make every Catholic, or even private, school like that. I taught in a Catholic school for a year before I met DH and I loved what I saw there. The kids were happy and innocent, just like how kids should be. They were taught so much more than just religion.