“And the children of the Kenite.” That is, the Kenite people. They went with the people of Judah and it seems they were at least to a certain extent assimilated into Judah.
“City of Date Palms.” The palm trees in Israel were date palms, not coconut palms. The City of Date Palms is Jericho.
“which is in the Negev of Arad.” A powerful town in the Negev of Judah. The “wilderness of Judah” was large and in several geographic regions of Judah, so it makes sense that the text would specify the wilderness of Judah in the Negev.
“lived with the people.” That is, the Kenites lived with the people, Israel, but specifically the people of Judah.