I think Eves baby dies and it's just a red herring - perhaps she lost it whilst trying to save "Alice" in an accident like the theory of the shed going on fire hence the scars and Matthews guilt too?
Confused how matthew nearly lost the dad his job
Or maybe they didn't believe she was alice later in and it turns out she was when she died and that's the guilt? That they doubted her
Perhaps they tried to "test" her somehow and that's how she dies?