I would go along with it - this is my family after all and I encourage creativity. But depending on the interruption, they might hear an answer that rings closely with "that can wait until I get home" or "don't hit her back, but try to resolve it between yourselves".
You need two hats. A work hat and family hat. This is the only possible social cue that will work in the long term.
I would completely expect my family to get behind this. I've worked remotely for many years now so my kids were (in theory) well trained to not bother me while I'm working. However, that started to get more lax post-covid. I also used to specifically work late at night and in the morning while they were at school. As they get older and stay up later, it has gotten more difficult to keep that schedule.
I recently moved my office to our third floor space. I'm hoping the extra work required to go up a flight of stairs will limit spontaneous interruptions during the day. I'm hopeful, but don't expect it to work long term.
I feel like this only makes sense in the US. As a non-US person, I still find it weird when people show up on video calls wearing hats (e.g. caps) at home.
