So, should the provider not ever go on vacation?

That would be a time that the parents would have to find alternate child care. Or what if she is injured or sick? What then? Providers need time off, just like other workers. If you don't want your provider to have time off, you need to pay the big bucks for the center, where your child will get less one on one and have colds and viruses every few weeks that keep
you out of work. I think people want to have their cake and eat it too.
I am thinking I need to call the families I used to sit for and thank them for being such good "employers".

I got time off and they let me take their child(ren) to the park, pool, mall and anywhere I went. I treated them like they were my kids and the parents appreciated that extra I gave them. We treated each other with respect and I truly enjoyed my job.
I am assuming that if the parents had originally said they didn't agree with the VBS plan, the OP would have either taken it as a vacation week or told the church she couldn't do it. The parents agreed 6 weeks ago, so I don't think the OP was out of line. If they weren't sure, they should have told her they needed to think on it for a few days.
OP, sounds like you have found a middle ground.

I am sure your church and all the parents of the children you will be teaching are very appreciative of your volunteering.
Marsha