Bascom Slemp owned a Pierce-Arrow, according to the Wikipedia article on the car. There probably weren't too many Pierce-Arrows around Congressman Slemp's Lee County, Virginia, home.

Both cars are Pierce-Arrows, with their distinctive fender-mounted headlights.

I believe this to be September 9, 1924. Coolidge and the First Lady went to Bolling to greet the pilots (Wade and Smith) who made the first aerial circumnavigation of the world. Coolidge's secretary C. Bascom Slemp was also reported to have attended according to the NY Times (9/10/24). I'm almost certain that's Slemp behind the first lady. The NY Times also reports that it was a rainy day and that many flags were on display, which you can see in the background here.

Granted that Coolidge was not a "smiley face" at the best of times, 1924 was not exactly a time when the Coolidges would have too much joy in their lives. In July 1924 their younger son, Cal Jr., died as a result of blood poisoning that developed after he played tennis barefoot on the White House tennis courts with his older brother. Based on Mrs. Coolidge's clothes this photo probably dates from before that event, but it's generally felt that his son's death left Coolidge even more withdrawn than he normally was.

We can see two of the men holding their hats over their hearts. The men in the background are bareheaded. They were showing their respect to someone or something - any idea what it was?

Old Cal was not exactly a smiley face. He was succeeded by Herbert Hoover, another sourpuss. Then came the Depression. No wonder the charismatic FDR was elected four times.