The difference for many people is more than a ten minute commute. I'd enjoy 20 minutes a day of quiet time, but in my situation it'd be an hour per day.
The trick to making family understand when you're on the clock is training them to treat the closed office door as though it was locked. If you come out of the room, your attention is free game at that point, but once that door is closed, you're not home. Takes awhile of effective communication and discipline, but once enforced makes remote work incredibly enjoyable, even with family at home.
That makes it hard to come out of your office to accomplish a specific task, like grabbing coffee or visiting the restroom. Then your attention's not free game, and you still have to sneak around.
...until summer rolls around...
Having worked from home when only a partner OR 2 kids were present, I can only imagine the additional pressure faced by that situation.
But speaking as a single parent of school-aged kids, summer vacation is... a challenge.
I come in to the office every day because my wife stays home with our 3 kids. Work from home when home is four people that want your attention doesn't work out very well. The few times I tried it, everyone just got frustrated that I was present but not available.
Maybe in a couple years when the kids are in school working from home will seem appealing. Honestly a ten minute commute and the entire office to myself twice a week isn't half bad.