Priam, Hecuba, and a dozen Hectors
This is an allusion to the story of Homer’s Iliad, in which Priam is the king of Troy, Hecuba is his wife, and Hector is his son, the most talented of all the Trojan warriors. Priam and Hecuba had nineteen sons and several daughters; they are being compared to Mr. and Mrs. Quiverful, who have a large family of twelve children themselves. Trollope is making the somewhat humorous point that both Priam and Mr. Quiverful are in the position of providing food for a lot of mouths. [MD 2005]
There is the further humor that results from the unlikeness between the royal family of Troy and Mr. Quiverful’s rather humble domestic unit. [RR 2011]
Source: Cassell’s Dictionary of Classical Mythology.