The best explanation for the King of the South/King of the North stuff in Daniel is understanding it in the context of the events leading up the Maccabean Revolt.
The King of the North refers to the Seleucids (Greek Syria, after the dividing of Alexander’s empire), most specifically to Antiochus IV; the King of the South refers to the Ptolemies (Greek Egypt, again after the dividing of Alexander’s empire).
A refresher on Old Testament history:
The Kingdom of Judah was conquered by the Babylonians resulting in the destruction of Jerusalem and Solomon’s Temple. Thousands of Jews were taken away into captivity in Babylonia. This lasted for roughly 70 years when a coalition of Medes and Persians overthrew the Babylonian Empire. Then under the rule of the Persian emperor Cyrus the Jews were permitted to return to Judea, to rebuild both Jerusalem and the Temple. Judea became a satrapy (a province) of the Persian empire under the satrap (governor) Zerubbabel. This is why the first stage of the Second Temple is referred to Zerubabbel’s Temple, because he oversaw its reconstruction during the time of Ezra and Nehemiah.
If you have a Protestant Bible, this is about as far as the history goes before we jump ahead to the birth of John the Baptist and Jesus in the Gospels. Though Catholic and Orthodox Bibles contain some books, most importantly here the book of 1 Maccabees, which provides some important historical information (and whether you consider 1 Maccabees to be Canonical or not is irrelevant here, the point is its historical value in this case).
So some more history: Alexander succeeded his father Philip, the King of Macedonia. Under Alexander Macedonia grew immensely, after several centuries of conflicts between the Greeks and the Persians, Alexander took on the Persians, first conquering Egypt, then the Levant/Syria, and continued right through Mesopotamia and reaching India. Alexander never took India, and at the age of 29 died of alcohol poisoning (or that’s the best guess historians have). In the wake of Alexander’s death his great empire eventually collapsed because his generals fought amongst themselves. Resulting in several successor states to Alexander’s empire.
The two most important for our purposes are the Ptolemies who took Egypt, and the Seleucids who took Syria. This is known as the Hellenistic Period of Jewish history, and Judea was now subject to a Greek kingdom, specifically it was under Ptolemaic control. And while things weren’t perfect under the Ptolemies, the Jews were largely left alone and they were able to practice their religion.
Several wars were fought between the Ptolemies and the Seleucids, a series of six wars known as the Syrian Wars. And each time Judea was basically between the crossfires. But it wasn’t until the sixth war, when the Seleucids under Antiochus IV (surnamed Epiphanes) took control of Judea from the Ptolemies.
Unlike under Ptolemaic rule, Seleucid rule was harsh; the Seleucids forced all subjects to be fully Hellenized–to adopt Greek culture, customs, and religious practices. That meant worship of the Greek pantheon. The Jews resisted, refused; some Jews did Hellenize (hence the presence of Hellenized Jews mentioned in the New Testament) but most Jews especially who were in Judea resisted. This led to harsher laws against the Jews, Jews were forbidden from observing the Sabbath, from circumcising their sons, and it became increasingly oppressive.
But the worst thing that could have happened, happened. In the Holy of Holies, the inner sanctum of God’s Temple, a pig was sacrificed by a Pagan priest in honor to Zeus. This is what the author of 1 Maccabees calls the “Desecrating Sacrilege” and what is mentioned by Daniel as “The Abomination that causes Desolation”. This act was the straw that broke the camel’s back, and led to a full on rebellion under the brothers Judas and Jonathan, given the name Maccabeus “The Hammer”, hence the term Maccabean Revolt/War. And, ultimately, the Maccabees were successfully, they liberated Judea from Seleucid control and for the first time in centuries the Jews were independent. This lasted until the Roman general Ptolemay (during the time of Julius Caesar) conquered the Maccabean Kingdom, the Hasmonean Dynasty was destroyed, and in its place the Romans had Herod (Herod the Great) made king, to serve as a puppet for the Romans.
Bonus fact, Herod was an Idumean (aka Edomite); the Edomites were forcefully converted to Judaism during the Hasmonean dynasty.
So Daniel’s prophecy seems to make the most sense in this context.
Of course in the Olivet Discourse Jesus pulls directly from Daniel’s reference to the Abomination to describe what was going to happen later, when the Temple would be destroyed by the Romans. This is likely a reference to the desecration of the Temple when the Zealots took over Jerusalem, and slaughtered all the priests, Josephus tells us that the Temple was literally soaked in the blood of slain priests; and that by the time the Romans accomplished their siege, the Zealots had already done most of the dirty work from the inside, and Rome merely finished the job.