How does Lily's illness change Alice's relationship with Haskett in the story, The Other Two?

When Lily becomes ill, the Waythorns and Haskett all have a vested personal/moral interest in comforting her and re-securing her health. One side effect of these events is that Haskett becomes more present in the Waythorns’ lives, thereby creating some awkwardness and discomfort given his and Alice’s past.