The Kane siblings had always been close, but as the years stretched and life pulled them in different directions, the moments they stole together became treasures—small, shining, and full of the kind of love that only grows between people who’ve shared the same backyard rink, the same holiday dinners, and the same parents’ quiet pride.

One crisp February weekend, with Lily home for a rare long break between her pro rookie season in Boston and an upcoming international tournament, ...