She may have thought he wouldn't be safe or well taken care of with his father, especially if she had planned to kill herself. Nothing specific points to that here, but it is sometimes a factor when mothers kill their children--they think they're helping them. Though murderers who love their victims typically don't leave them naked in the woods.
I'm a bit confused by the locations of everyone in the family over the past few years... all three moved to OR and lived in the house together for Angela's work. Then a year, year and a half ago, Angela and Amos split and Amos moves back to OH. Then at some point Angela and Joshie move to UT and live with a friend? What's going on with her job at that point? She drives a porsche so she must not be doing that poorly, and on top of that she retains ownership of the house she and Amos bought, because she and Joshie move back to OR just a few weeks before his death. And all the while social services is investigating, but Amos doesn't particularly seem clued in to that?
It's all quite bizarre. May not be mine to know, but I don't understand Amos just leaving Joshie. Would be insightful to know if he has custody of his other kids.