“After some years.” The Hebrew is an idiom; the text more literally reads, “At the end of years.”
“the daughter of the king of the south will come to the king of the north.” There were continual periodic clashes between the Seleucids in the north and the Ptolemies in the south, in Egypt. After the death of Ptolemy I in 285 BC, Ptolemy II Philadelphus (285-246 BC) took the throne in Egypt, and about 250 BC made a peace treaty with the current Seleucid ruler, the grandson of Seleucus, who was Antiochus II Theos (261-246 BC). Under the peace treaty, Berenice, the daughter of Ptolemy II Philadelphus, was to marry the Seleucid king, Antiochus II, and then after Antiochus II died, the Seleucid throne would be given to a child of theirs. The phrase “come to” in this context means for a woman to go live in the man’s house; i.e., marry the man (cp. Josh. 15:18).
The plan failed. In order for the treaty to work Antiochus had to divorce his wife, a powerful woman named Laodice (or Laodiceia), and exclude his two sons by her from the throne. But Laodice managed to have Antiochus, his new wife Berenice, and their child, all killed. Thus, Berenice did not retain the “strength of her arm,” that is, her power, and neither did Antiochus, who strengthen her in those times. Furthermore, Berenice’s father, Ptolemy II, died about that same time.