For me I don't think that it is relevant for you to inform your family your source of income except the wife because informing your family your source of income is like someone who is letting everyone in the family to know the method he or she applies to make money so I don't think that it knowledgeable from my own understanding of investment method and also a business method because not everyone in your family can be happy for you to succeed in life I'm not everyone that we like you to be great for life so that is why it is not good to review your source of generating income to your family people
You are probably referring to the extended family because I don't see any reason why your siblings or your parents wouldn't be happy for you if you are earning money while sitting at home. I work online as well, and my family has always been happy and supportive about it. I never needed to explain much to them, but when I withdrew my first earnings from my online work, that was enough to make them realize that I wasn't just wasting my time sitting in front of my computer all the time.
At first, your family, especially the elder ones, would think that you might be playing games or watching movies if they see you using laptop or computer all the time, but if you show them that you are earning money from the time you are spending then it becomes understandable for them and then they would never say anything to you regarding it.
As for the extended family, you don't need to tell them anything.