This reminds me of a detail I once read in the Hollywood, Interrupted book. There was a section about the famed Crossroads school which is a strictly art and theater school in Los Angeles. So of course, celebrity children are commonly students there.
One detail had a teacher talk about the students, specifically ones who are children of famous people. Elliott Gould's son got a mention. Apparently Elliott Gould never went to any of his son's events, and it seemed like he wasn't involved with his son's activities at all.
It made me think that this isn't an uncommon thing, and might be why so many have problems. Their parents aren't around.