The Ice Twins by S.K. Tremayne

Sarah and Angus Moorcroft suffered a horrible loss fourteen months ago when their six-year-old daughter, Lydia, died. Wanting a new start, they decide to move from London to Torran, an island that Angus' family owns in the Hebrides, with their surviving daughter, Kirstie--Lydia's identical twin.  When Kirstie tells Sarah that she's actually Lydia and that it was Kirstie who died, Sarah wonders if it's true.  Chillingly enough, there is no way for Sarah to medically prove which twin died because the girls DNA is same and they were never fingerprinted. As Sarah tries to come to terms with Kirstie's confession and think of another way she might uncover the truth, Kirstie--who insists she be called Lydia--begins behaving oddly. Sarah's and Angus' relationship also begins to splinter with Kirstie's revelation. With the isolation of Torran and rumors of ghosts, the Moorcroft family sees their lives unravel...  This novel of psychological suspense is similar to The Hidden Girl by Louise Millar, Beneath the Shadows by Sara Foster, and Hold My Hand by Serena Makesy.