I have to say, I absolutely love and adore KawaiiStacie's Education System Overhaul mod which has some of the features you've mentioned.
Features:
Preschool: Your toddlers go to preschool and learn toddler skills there, as well as having needs taken care of and gaining character values! (Unlike Day Care in the base game, where they learn nothing--if you want to work on toddler skills while parents are at work you have to hire a nanny.)
Grade school and high school: Your children and teens get real skills from school and homework! Children pretty much gain everything but motor, while teens gain mostly logic and writing with a bit of fitness (PE?) and cooking (home ec?) (Unlike base game, where they learn nothing from school or homework and it eats up their day without any benefit beyond not having them taken away for neglect.)
Homeschooling: OH MY $DEITY do you know the bug where if you go into CAS while kids or teens are at school they sometimes come home early and lose responsibility? (Especially if the parents had a club gathering going when they left, but I've had it happen without.) You can give your kid the "home school only" PC and they can attend online lectures and not miss out on school when the bug brings them home early! (There is no in-game homeschooling.)
The only downside is that KawaiiStacie has taken down all her mods for updates (which Better Exceptions has been complaining they need) and it's not currently available. However, Sims Team, if you wanted to incorporate some similar features.... This mod is once again available!
