Fausset's Bible Dictionary
Ain el Weibeh in the Arabah, 10 miles N. of the place where Mount Hor abuts on that valley. Three fountains issue from the chalky rock. Here wady el Ghuweir affords access northwestwards through mountainous Edom; from here accordingly Moses sent to ask a passage through Edom by "the king's highway." Barnea = "son of wandering", i.e. Bedouin (Furst). "Country of convulsion," compare Psalms 29:8 (Speaker's Commentary). "The wilderness of Kadesh," i.e. the desert adjoining Kadesh; the northern part of the Paran wilderness was called Zin (Numbers 10:12; Numbers 13:21). The encampment from which the spies were sent and to which they returned (Numbers 13:26; Numbers 32:8); sometimes called Kadesh alone. Meribah Kadesh is the same (Ezekiel 47:19; Ezekiel 48:28 margin; Joshua 15:3; Joshua 15:23). The encampment at Kadesh is called Rithmah from retem , "the broom," the most conspicuous shrub of the desert (Numbers 33:18).
Probably the encampment at Rithmah was during Israel's first march toward Canaan; that at Kadesh was in the same locality, though on a different spot, 38 years afterward, in the 40th year, when they were about entering Canaan. The ancient name of Kadesh was En Mishpat (Genesis 14:7). El Ain (identified by some with Kadesh because this site is called Gadis and the neighbouring plain, Abu Retemet, is like Rithmah) is too far N.W., 70 miles from Mount Hor and 60 from Mount Seir; but Kadesh was only one march from Mount Hor (Numbers 20:16; Numbers 20:22; Numbers 33:37), "on the edge of Edom," "on its uttermost border"; on low ground (whereas El Ain is on high ground) from whence the spies "go up" to Canaan. A line drawn from E1 Ain to the river of Egypt (Joshua 15:21-27) would cut the middle of the Negeb, and so cut away part of Judah's inheritance. The true Kadesh must be more S.; Petra or Selah was too far in the heart of Edom to be Judah's frontier, and "in the uttermost border of Edom."
However, Palmer identifies Kadesh with El Ain as "one of the natural borders of the country; the Tih, a comparative desert, the Negeb or South, Palestine, and Syria forming an ascending scale of fertility." The encampment at Rithmah (Numbers 33:18-19) was in summer the second year after the Exodus (Numbers 13:20), that at Kadesh in the same district the first month of the 40th year (Numbers 20:1). At the first encampment Israel stayed probably for months; they waited for the spies 40 days (Numbers 13:25); Moses and the tabernacle remained (Numbers 14:44), while the people vainly tried to reverse God's sentence and to occupy Canaan (Deuteronomy 1:34-46): "ye abode in Kadesh many days" (a long indefinite time). Then Israel "compassed Mount Seir," i.e. wandered in the desert of Paran, until all that generation died (Deuteronomy 2:1).
In this period were the 17 stages, Numbers 33:19-36. Lastly, Israel again was at Kadesh in the first month of the 40th year, and stayed for three or four months (Numbers 20:1-22-28; Numbers 33:38). Here Miriam died and was buried. Here water failed, and Moses by impatient striking of the rock, attribution of the miracle to himself and Aaron ("must we fetch," etc.), and unbelief ("ye believed Me not, to sanctify Me") in the goodness of God to an unworthy people, dishonoured God, and he and Aaron were adjudged the penalty of not entering Canaan (Numbers 20:12-13; compare Psalms 106:32-33). From hence Moses sent to the king of Edom (Numbers 20:14, etc.).
On the messengers' return Israel turned from Edom, leaving Kadesh finally, and after Aaron's death at Mount Hor marched around Edom to Moab (Numbers 33:41-49). Kadesh ("holy") may have been named from the long presence of the sanctuary and priests. En Mishpat, "fountain of judgment," corresponds, judgment and sanctity emanating from the one divine source. Meribah Kadesh, "strife," is a perversion of judgment; the opposites in the one name marking graphically the sad events connected with Kadesh. Kadesh gradually sank to its original obscurity as a watering place for the nomads of the desert. The cliffs at the mouth of wady el Ghuweir near Ain el Weibeh, and in front of the host in marching eastward through Mount Seir, may have been the scene of Moses' striking the rock (cela , not tsuwr ) (Numbers 20:7 ff). Merely certain occurrences and enactments are recorded of the 38 years' wandering, in Numbers 15:1-19:22.
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Fausset, Andrew R. Entry for 'Kadesh Barnea'. Fausset's Bible Dictionary. https://www.studylight.org/dictionaries/eng/fbd/k/kadesh-barnea.html. 1949.