what generalization can you make about the gods and their hero children

The Gods don't have a lot of contact with their demigod children. I’m not sure if they really care all that much about their children: they have many as I recall in Greek mythology. They seem to only notice them when circumstances intrude on their God-lives.

Well,I wouldn't say the gods don't care for their children. Sure, some gods may not, but others, such as the big three (Posiedon,Zeus,Hades) do care about their kids. They may or may not say this out loud, but will give them help, a nudge in the right direction, or information when their kids need it most. The gods that you will see that don't care very much are Ares, Demeter, Hermes, and most of the minor gods. However, one thing that you can always be sure of is that the gods never get married to human beings, so their children are (as much as I hate to say this) illegitamate. Also, all demigods have at least some form of ADHD, dyslexia, or both.