Hi, you raise some good points and I've experienced the same issues as you over the last few years that I've been experimenting with fasting. The benefits achieved by the Master-Cleanse is basically due to the fasting aspect of it. While it's hard to find scientific research on The Master Cleanse itself, there is a lot of scientific research on the physiology of fasting and juice fasting. You can start by researching fasting in scientific databases such as PubMed or recommending your family do that if they are that concerned. Also, here's some good online links:
Those are quite basic but you can find more scientifically based articles by searching scientific databases for fasting. Also, there are some good in depth books on fasting by Paavo Airola and Steve Meyerowitz. I don't think fasting is too "new" to the modern medical world, I just think modern medical practioners can't benefit financially when people are taking charge of their own health by alternative practices like fasting, so there really isn't much drive towards this aspect of research. Modern research is all driven towards creating medicine that is profitable, like drugs, but not necessarily healing.
As far as family and friends, I've found it best for myself not to mention or discuss what I do with them at all or they'd drive me crazy with their negativity. They aren't in the position to want to understand or be supportive of cleansing, so I've found it best to keep it to myself. They will see for themselves later that you are doing something right when your health improves and theirs probably doesn't. Also, I agree that taking yourself off the fast is very, very difficult. But if you can get through that part okay then the benefits will be well worth it. Good luck and congrats on making it through 14 days!