But back when I worked in a "real" office, I had the exact same situation you just described. It was just as noisy and loud as it is here at home.
In either place, I have to learn how to work with distractions in the background, and learn how to ignore them efficiently. So why not do that at home?
Here, I have an "open door" policy, so that I can help my wife out with any homeschool tasks that might be better suited for me.
It can be challenging sometimes, but it's extremely rewarding.
And I'm just as productive here (if not more productive) than I ever was at a "real" office.
But YMMV.