So I was playing around in the school module and trying to set it so that homeschoolers only have to do homework during the week, and I was able to adjust in the XML for a Monday-Friday schedule and that part worked, but they constantly showed the 'Missing School!' dialogue on the career page and dropped from straight A's to F overnight. I don't mind toggling the enable/disable homework option for them, but that gets tiresome when you have multiple kids and are trying to keep track.

Is there a way to modify this without breaking school performance?

If you toggle the homework option on and off, you will find (I think) that all of the students' school performance will keep getting reset to 0 in between. I believe the underlying problem, as you suspected, is that their kids' school is actually City Hall rather than a "real" school and there are no set hours/days for school to be "in session" -- it's all the time 24/7 or nothing for homeschoolers. Let's see what our developer or others may have to say, but I don't think there is a simple XML adjustment that will make that work quite right as can be done with the mod's specialty schools and the times that they actually convene.

That makes sense. Honestly I figured if it were as simple as that it probably would've been coded that way originally, however I have an incurable need to tinker with things to see how they work, haha.

Just as an FYI, it's not really a problem, when I replaced the altered version with the original version of the schools module, the in-game interaction for downloading homework shows as 'Nraas.Careers.HomeSchooling:InteractionMenuName' instead of as 'Download Homework' now, although I deleted my caches in between. It's not a problem for me, though I suspect it's probably not how it's supposed to work after such a change.

You do realize that you have performed the equivalent of tearing the tag off of a mattress that says "Do not remove under penalty of law!" correct? Stay where you are, remain calm, the proper authorities are being notified.

I do so gleefully with every mattress I purchase I should probably admit here that I'm a web developer by trade so poking the code to see what happens is literally how I make my living, haha.