As a private school they do not have to follow the IL state requirements for PE to give her a diploma or credit. So it is up to the private school and their private school rules. Private schools and homeschools are categorized the same and IL law just states "providing an education comparable to IL public school" and clearly you provide 45 minutes of daily physical education (and more!) so your child is meeting this.
For those in public school:
What is confusing is that IL mandates PE *daily* for kids in K-12 BUT it isn't a graduation requirement!?! How does that work??
It also allows for substitution of PE for other activities, sports, band, cheerleading, JROTC,. You would think gymnastics would qualify for it and I would push the issue since clearly gymnastics is at least if not more physical than those listed.
This was not an issue so far during elementary school for my son but now since he is entering middle school 6th grade I will be pushing the issue and it seems I have the law on my side.
Wish me luck on Monday when I go and talk to them about half day and of course no PE! And I wish you the best too!