It's too bad this is a new school because that means they probably have a lot of high-minded plans, but no track record for you to actually check out. However, I do think that based on what you've learned form others about your local public school, I'd be inclined to avoid it--so if this is your only other option, I'd want to try it.

That said, since your child is only 3, it seems like you'd expect to have at least one year of experience to go on before your child could expect to attend?

I think the question about what one does in the 3rd grade is going to come up almost anywhere. My DD is in 3rd now in a regular public school (K-6) but just because the school has those older grades doesn't mean it's easy to actually use their materials. After 3 months of trying to keep up with DD's math we've decided to try an online math curriculum--and IMO, math is one of the easiest subjects to accelerate for a kid who can learn independently.