It's a safe bet to say there is more than one goofball who is dead or crippled from dripping and driving.
Before a few months ago, I associated e-cigs with shysters at mall kiosks selling 100 dollar penlight battery sets. Many people I talk to offline seem to have the same idea.
Yeah, the local mall kiosk sells a single joye 510 battery, with PCC and two atty's for $150. It's just plain terrible. I like to stop by with my stuff when I see other people stopping, and "sample" their terrible juice just so I can guffaw at their prices passive agressively.
Still, I agree that the name "e-cig" is a misnomer, and quite troubling. I find myself explaining that I am not using tobacco, not producing smoke, and so on, all the time. I'm not worried about any of the "conspiracy" nuttiness, really. The bad rep is simply due to innocent ignorance, and education is the best way to rectify it. Your answers to your family were the right ones, and the only way to improve them is to learn and share better information regarding battery safety. Never hurts to know the basic chem too, but if that's too much of a chore, at least know that you're vaping food flavoring, and food additives. Let them know that you are aware of the risks of vaping, and explain that the risks of continuing smoking are much greater.
Nothing is risk free, even oreos. I have a mild heart condition, and nicotine isn't great for me personally, but fatty foods and stress are worse, nevermind the fact that I'd still be smoking combustion cigs if I hadn't stumbled into vaping. It's not as safe as quitting nicotine altogether, but it's absolutely safer than being overweight, overstressed, and inhaling smoke of any kind. Generally, being honest about the big picture will make people feel more comfortable. The last thing you should do is say "I'm only inhaling water vapor" or other such easily rebutted claims, or go on about un-provable conspiracies.
How am I improving the reputation of vaping? I am polite (I put the PV away first when asked, then explain the difference without arguing), educated, and I vape openly.
Be the change you want to see, and the reputation will follow naturally.