It's fruitless and needless to try to change other people to a given point of view. All you can do is present your views, opinions, feelings, and facts and see how they respond. Any change in your family's opinions, if they come at all, is probably going to result from seeing you thrive on the diet. You don't have to do fruit-based if that's impossible in your current situation. You can do the second-best thing: starch-based (Dr. McDougall style). It's still high-carb, low-fat vegan and you'll still feel good.
In terms of getting support, you should check to see if there are any vegan/raw-vegan/fruitarian meetup groups or facebook pages for your area.
All the best!
Can I politely ask how old you are? Are you purchasing your own food? If you are, you don't need anyone's opinion on what you choose to eat. I agree with Z3F, it's useless to try to explain or change others views. If eating or buying a lot of fruit is not doable, start out on a Raw Til 4--banana smoothies for breakfast, bunch of fruit for lunch and a starch dinner (potatoes, rice, corn pasta, steamed veggies, no oil, no salt). This is a great way to transition into fully raw, especially if you are a new vegan. You're not going to get any support from your family initially. For some people, 30Bad and youtube are the only supoort for this lifestyle. Instead of trying to explain the whole philosophy of this lifestyle to them, just tell them you're experimenting with eating more fruits and veggies for health and to see how you feel. Even meat eaters heard somewhere that fruits and vegs are good for you lol! Trying to explain raw to them will blow their minds at this point. Good luck, take it day by day; if you have to eat cooked, choose the rice, veggies, sweet potatoes and of course the salad option.
Just address it to them as a diet to help with whatever area you are needing...no one second-guesses a diet, but will constantly bombard you with opinions, questions and attitude if you say it's a lifestyle. Once you feel established then you can discuss it more...just do your best, keep a log so you can see what causes problems and what you eat on your best days! Temptation will always be there so CARB UP and just keep getting up and don't give up! :)