Abuse by teachers within schools is not on the rise. Abuse within homeschooling families is also not on the rise. As I said. But homeschooling in general IS on the rise and fringe people are attracted to it.
The question is how do we protect kids within those families? Kids in public schools have multiple safety nets. Homeschooling kids do not.
I was just reading a study last month about abuse (not just sexual) from teachers being on the rise. I will try to go find that later tonight. (Not that it's relevant to this family.) People who actually homeschool have plenty of safety nets. They take their children to the doctor, dentist, their children attend classes and lessons, they are in sports, they have well developed social circles, etc.
The problem is the people who aren't actually homeschooling. They are abusing their children and isolating them under the guise of schooling. I honestly do not know how to protect and find those children. People who inflict these abuses on kids are going to hide them from society in any way they can. The fringe folks are hide to keep track of, period. It helps for neighbors and family members being aware. I would suggest that there were opportunities to protect these children. Family members cutting off ties to their children is a huge red flag.