The Arkwrights are the people who agreed to foster Aidan Cain right after his grandmother died. They are a very conventional family, set in their ways and their expectations. Mrs. Arkwright keeps asking Aidan over to let her give him a cuddle, which he never wants to do. She also evidently tries to make him forget all about his grandmother as a cure for what in her mind is undue grieving. And everyone in that family thinks of him and addresses him as "Adrian".
Although the Arkwrights aren't exactly bad people, they have very little empathy or understanding of anyone else's feelings. The other foster children at the house, though, do support Aidan, but none of them seem to have the ability to protect him from the Stalkers, so he runs away.
When later in the novel Andrew Brandon Hope visits the Arkwright home to get a better idea of what happened to Aidan between his grandmother's death and his arrival at Melstone, he very quickly determines that their misunderstandings and constructed memories of what went on should be tolerated, and he tells them conventional, normal-sounding tales of how he got involved in Aidan's case and where Aidan might be now.
Not bad, but clueless. That should be carved into the gravestones that are eventually used for their cemetery plots.