Not sure if having the same issue as I was, but I was way behind on the kate side and was catching up this week and got stuck on private lessons with karen too. For me the issue seemed to be that once Max goes to school it no longer triggers. Luckily I keep a lot of saves, so I rolled back to one of the late anatomy class steps just before he arrived, only doing private lessons on Tuesdays and skipping everything else to not advanced the story, and was able to finish the entire investigation questline and then continue on with swim / alt punishments