I agree. If your family members are those that see every online business as illegal then it's better to look for a branded name to call yourself or a word to describe your work. You can also tell maybe one or two people you trust to understand and not tell the rest about your real source of income.
Then, I agree with not telling them the exact amount you earn, instead, give them a figure range probably lower than what you earn to avoid unnecessary monetary attention. Also, if you stay with your family members who may not understand your kind of work, try making use of the hub sometimes or going to a friend's sometimes. So they won't be seeing you indoors on your laptop all day, which can increase the questioning.
But I doubt they would think about negative about what you do online especially that online jobs is now booming. For sure they already hear that earning online exist. What you need to do is to show them your online gigs and tell that everything you do is legal.
We cannot erase some facts that they might question on how we can generate money online, but if we make them understand the nature of our job then for sure they could able to get an idea that what you do is good then maybe you can influence your brothers and sister to do the same also earn at home by help of current technology.
But total earnings should be hidden and we should not teach and show them everything since maybe that actions will create a trouble in our side.