Here's my best, last thought. It was Lori.
1. John is the father. Erin wanted her best life for her child so she blamed the dumbfuck kid who had rich parents because she felt they would always pay and she was sleeping with him at time. That's better than her uncle going to jail for stat rape and the incest. When the kid is in on the catfish and assault, she's done with this bullshit as she just wants her kids ear surgery and threatens to out John (which Lori hears).
2. Confrontation at park where John, Billy, and Lori are - Lori pulls out gun. Billy tries to wrestle it from her, but it goes off killing Erin or Lori just flat kills her.
3. If you go back and watch John's last conversation with Lori he talks to her about doing things for the family and asks her whether she can lie to Mare for the good of the family. This conversation makes a lot more sense if Lori shot Erin and John is going to kill Billy to help cover it up.