“set his face.” This is a Hebrew idiom for “resolve,” “firmly decide.” Antiochus III the Great decided to make a treaty with Ptolemy rather than face possible conflict with the growing power of Rome.
“terms of an agreement and will perform them.” Instead of pressing on to an even greater military victory after defeating the forces of Ptolemy V Epiphanes in Sidon, in 197 BC, Antiochus III the Great opted to force a peace treaty upon Ptolemy. This was due to the growing influence of the power of Rome. Antiochus feared that if he attacked Egypt, Rome might intervene.
“he will give him a daughter of women to destroy the kingdom, but she will not stand with him.” As part of the peace treaty of 197 BC, Antiochus III gave one of his daughters, Cleopatra, to Ptolemy V Epiphanes in marriage. Basically, Antiochus forced his daughter upon the young Ptolemy, who was still under ten years old. Antiochus planned to have Cleopatra undermine Ptolemy V, but instead she loved her husband and stood with him against her father, even working to make alliances with Rome as a way of protecting the kingdom.
Antiochus’ daughter Cleopatra was the first Cleopatra of Egypt, not the famous Cleopatra of the movies. The famous Cleopatra was Cleopatra VII Philopater (c. 69-30 BC), who lived more than a century after the first Cleopatra. Cleopatra VII was the last queen of Egypt (her son Caesarion reigned as Pharaoh for less than a month after she died), then Rome took control of Egypt.
The phrase, “a daughter of women” is more literally in Hebrew, “a daughter of the women,” which is an interesting and uncommon idiom for “a daughter.”