I'm late to this thread, but I knew the Petersons. They lived three blocks away and attended St. Patrick's Church. My sisters and I used to babysit Heidi and her little brother along with other kids during mass. Her disappearance caused absolute terror and sorrow. We were advised not to play in the trees and bushes directly across from the park for fear something bad would happen to us too. And after her remains were found half a block away among the blackberry brambles by the freeway, rumors spread.
My mom told me a few years before she died that she had been friendly with the mother of the boy(s?) suspected of killing Heidi. They attended our church and lived quite close to Heidi and the site where her remains were found. Mom told me she thought the son or sons had done it based on some observations about things their mother said and did afterward, and the fact that they moved shortly after the murder/discovery...but this is hearsay only. DNA evidence would surely have solved this by now.
To illustrate how deeply this murder affected kids at the time: I went to a grade school reunion literally 32 years later...and the first thing a classmate said to me was, "Weren't you the one who was babysitting Heidi when she disappeared?" (No, no I wasn't!) But wow. Clearly this had an impact, or she wouldn't have mentioned it!