Warwick appears briefly in Omeros but has a huge impact on the narrator and his thoughts about life and work. He first identifies himself as one "raised in this obscure Caribbean port,/where my bastard father christened me for his shire:/Warwick. The Bard's county" (XII.i.68). It's pretty clear that Warwick has passed his poetic sensibilities on through his blood—the Bard is none other than Billy Shakes himself—and this genetic mandate makes the work of the poem a deeply personal journey for the author-turned-narrator.
Warwick asks his son to recognize the importance of that genetic talent and to not forget the other part of his blood that should motivate all of his poetic endeavors: his people. As they stroll through the town, Warwick reminds his son of the people on the island who came before them and suffered to make a life for them. It's this vision of the women "ants" that Warwick wants his son to keep in mind as he writes:
"Look, they climb, and no one knows them;
they take their copper pittances, and your duty
from the time you watched them from your grandmother's house
as a child wounded by their power and beauty
is the chance you now have, to give those feet a voice." (XII.iii.75-76)
Warwick takes one more opportunity to drive home his vision for his son's life and to make sure that he understands the importance of his work. The narrator is not particularly grateful for Dad's second visit—it's cold, he doesn't really want to talk, and he's getting grouchy with age. But Warwick still charges his son with an old ambition of his: to travel to the great capitals of Europe, all those places in his books that he could not visit in his own too-short life.
But for the narrator, this isn't meant to be a pleasure cruise. It's a crucial part of his education and the fame of his entire island nation depends on it: "Once you have seen everything and gone everywhere,/cherish our island for its green simplicities […] The sea-swift vanishes in rain,/and yet in its travelling, all that the sea-swift does/it does in a circular pattern" (XXXVI.iii.187-188). In other words, the narrator has to come back, and he has to sing of his people.
The appearance of the father in this poem helps the narrator nurture the "inner eyes" and clarity of voice that he needs in order to sing of the beauty of his land and people. Without Warwick's insistence, he might have just found a picture of Homer to spend his days staring at.