If i may ask, what is your age range? You are still living at home with family?
If so, i can understand that you can not "lie" moral or not. If your family sits down to a meal, well.. your not sitting with them, its obvious.
Drinking juice does break a strict water fast, but depending on your reasoning behind the fast, i see no problem. Many juice and water fast, sometimes alternating days, its healthy in my opinion, but maybe go for the fresh squeezed, much better than bottled or can juices.