I do some in-home tutoring, and this sometimes means working in a family space. However, as a tutor, I also have to create a professional setting that allows the kid to focus and recognize they're working, not just hanging out at their dining room table.
Most parents get that and allow the space to be created, e.g. by chilling in the next room or working silently. But others will walk through with young siblings (very distracting!), put on a loud movie, come in and tousle the kid's hair, or urge them to do something that I don't particularly need but they see as the basics of hospitality: "How can you not have gotten your tutor a glass of water?" and so on. In one case, a parent has brought a kid to tears with scolding during a lesson. We lost a lot of time recovering from the disruption.
I have a few years of experience tutoring now, but I'm still not great at asserting the professional boundaries of a lesson. It's hard to overrule the fact that it's their house, their kid, and their money. Plus I'm young, being in my mid-twenties. (To be clear, these are objections I consider, not that I've been told. I rarely broach the subject.)
How can I communicate that despite those things, I need to set the ground rules?