Also, if that interview is really important to you, talk to the family. Move your seat. Talk from a coworking space, or from a park or similar public place provided that you have a headset; I did talk form a park, worked well.
To say nothing of these neat features of Zoom, Meet, etc that allow to put a virtual background, given enough CPU power.
Many conferencing programs allow you to set the background. Use a photo of a bookshelf and you're good to go!
A: An affluent individual with a dedicated home working space, high-speed and reliable broadband provider, and high-quality computer, video, and audio gear
B: A poor individual in a multigenerational household sharing working space with other household members on an ongoing basis and connectivity over flaky mobile service using a cheap Android device.
Which do you suppose might have an inherent advantage?
Would an on-prem working arrangement with employer-provided workspace, networking, and computing equipment increase or decrease any such advantage?
"your family in the background"
It's an easily resolved problem. I do it myself, as my office is a mess. I've used a photo of a bookshelf, too :-)
I've also had many business zoom meetings with people with their kid in their lap, or their pets demanding attention, etc. It's not a problem.
Which you still seem to be striving to neither acknowledge nor address.