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.
That's true but when it comes to parents I don't feel is all parents that would understand even if it has to do with money, you still need to explain further than you just said because some parents prefers to see you walking out every morning like every other young individual with some files and other things that's when they'll believe you without you saying much, just tell them you're going to work and that's it.
For the young ones they are the ones you can easily tell without thinking if they'd believe at first explanation or not because they have a more open mind that these sit at home job do exist, as for extended family I agree with you and I don't think such information should be disclose to them even in the dream😏.