Except Ann had already identified Jeremy as a threat to their livelihood, prior to the killings. I think she informed 'dad and Peter' of the potential threat? They haven't exactly gone in to immediate post-killings period with an open mind have they?
I don't think she identified him as a threat exactly? He wound her up and and took pleasure in it. The fact that she took her livelihood seriously and he as a bit of a joke, speaks volumes. She didn't like some of the things he said, one of them being that they would both soon be in charge of Osea - in retrospect, I guess that was a pretty chilling for her. As far as an open mind goes, they knew the characters involved and we don't - they clearly had reason to suspect him.