You should not include your family in your private matters if they do not support you with it. Now I am a very open person so I will tell people about when I fasted including strangers. Also I consider it my purpose to make fasting popular again like it was 2,000 years ago. The bible has 74 references to fasting.
As the story goes, the devil tried to stop Jesus from fasting. Of course it was his own doubts. But your doubts are supported by your family. Here is a rule I have. The more you care about what others think, the more unhappy you will be. To see if I am right with myself, see the page on site below-- Prescription For Happiness.
The more you know about fasting, the more motivated you will be. See site below with quotes by New England Journal of Medicine (on fasting for losing weight), 17 different MDs, Hippocrates, Mark Twain and Abraham Lincoln on Fasting and Lemonade Diet. I like this MD quote: "Fasting is profoundly simple and simply profound." Good luck with your fast and losing weight (site above has info losing weight also).