Your group is independent of the school, so if the school is an LLC that has no bearing on your group. We do suggest that you incorporate first then file for federal tax-exempt status. Here are some articles that will be helpful to you:
I'm the president of a small private school that is classified as an LLC (and intends on staying that way for tax purposes). As a PTO, we are considering becoming a 501c3 so that we can reap the benefits of a nonprofit. What sort of rules are in place for a PTO that is 501c3 giving to a private school that is not one as well?
I feel like I've seen this topic before in the Facebook groups but can't find it now.