The phrase "at that time" means the same thing as and intensifies the phrase "in those days." AT: "in those very days" or "at that very time" (See: [[rc://en/ta/man/translate/figs-doublet]])
Jehoshaphat, whose name means "Yahweh judges," was king of Judah before Joel lived. There is no known place with this name. It would be best to translate this as the name of a valley that people named after the man Jehoshaphat.
These two phrases emphasize how Yahweh views Israel as his own precious people. AT: "the people of Israel, who are my inheritance" (See: [[rc://en/ta/man/translate/figs-doublet]])
# traded a boy for a prostitute, and sold a girl for wine so they could drink
These are examples of the kinds of things they did and do not indicate what they did to two particular children. AT: "and did things like trading a boy for a prostitute and selling a girl for wine, so they could drink" (See: [[rc://en/ta/man/translate/figs-explicit]])