"Saranghae" is possibly the best way to say I love you to a close relative, however there are different forms with different levels of familiarity. "Saranghaeyo" is a general form.
Saranghaeyo is a polite way of saying "I love you" in Korean, which I think would be most appropriate for your situation. Another form 사랑해 (sarang hae) is usually used between lovers or between parents and children.
