It's not just your family. In much of the world, people (most especially your parents) will equate entrepreneurship with not having a job, scamming, all sorts of negative associations. But it's your family, so they will be somewhat forgiving. Show them what you're doing, point to the people in the world who have done well (de-emphasize the billionaires, and emphasize the people who created jobs for themselves). Be passionate. Like everything you do, you have to sell it to them.
I think the word "entrepreneur" has so many negative connotations because it's overused (at least in the States). Jobs are called entrepreneurial, employers are looking for entrepreneurs and MLMs like Cutco & Mary Kay consider their sales people entrepreneurs. It's sad.
I really like & use the titles cofounder or founder.
Now that you say that, until recently I resisted calling myself an entrepeneur, it does have a lot of negative connotations. I'm past that and now I probably should try and drag some of them along with the dream, they'll be kicking and screaming - at first anyway - but it's a whole lot better than grinding my teeth.
I too have noticed that being passionate about what you're doing, and getting that message across positively, really helps turn skeptical attitudes around.
I'd say anywhere where there aren't a _lot_ of successful startups compared to the number of "conventional" businesses, and a good startup community. Northern California, Massachusetts, and where I am now (Ottawa, Ca) are about the only places I can think of that don't have that stigma. But I haven't been everywhere in the world.
