"Oh , how I wish I could postpone my vacation! It is scheduled for the 7th of November and while I wish to go, I wish also that I could fast for at least 21 days, which wouldn't be wise since I would be ending the fast a day before my trip. Refeeding would be a disaster, no?"
Congrats on your fast so far, it sounds like you are doing great. Where would you be going on your vacation and what kind of accomodations would you have? Do you feel that juicing the first few days of your vacation would be implausible or even impossible? If so, yes i would recommend breaking your fast early so that you can juice for a suitable number of days (generally about a day of juice for every 4 days of fasting depending on various factors) before then having just fruit and veg for an equal number of days before transitioning into other foods.
"So...
Should I appease my family by switching to juice?"
If it was me and unless there was actually something wrong with my physical state 14 days or so into a fast (what is your specific situation by the way?), i would absolutely not appease my family (or anybody else) by eating. Your fast, your body your life, that sort of thing ;). I believe it would be very bad policy to stop doing something immensely good for my health because people misinformed on the subject of fasting believe I should. Instead i would attempt to educate them with some good literature and otherwise shoo them away :^)