Originally forbidden until 3 a.m. Monday, driving is now permitted after 8 Sunday evening. Police report a dramatic rise in calls to break up fights among families forced to stay together.

For Americans, nondriving Sundays are still a novelty; for many Europeans, they already are part of the regular round of life. Over the past month or so, six European countries—Belgium, The Netherlands, West Germany, Switzerland, Italy and just this week, Denmark —have flatly forbidden all Sunday driving, except for…