Is a longing family gaze after separation considered lustful and forbidden, and how can one distinguish between a gaze of lust and a gaze of love?

The gaze mentioned is not from lust, and it is not a forbidden gaze. It appears that the questioner is afflicted with some obsessive thoughts, and he should avoid and disregard them. As for the forbidden gaze due to lust, it is that which is accompanied by the arousal of lust, and this is a well-known matter that is inconceivable to emanate from normal individuals towards siblings and family.