The relationship between peace in heaven and peace on Ithaca and in Odysseus' household is that as a result of the gods' incessant manipulations of earthly matters, the Greeks had to rely completely on what the gods had in mind for them. Athena manipulates most of the plot of the epic, excluding the temporary interferences by the other gods, which caused the many conflicts for Odysseus. However, until Zeus points out Athena's weakness of meddling on earth and explains his idea stopping the fighting in Book 24, she relentlessly claims that was her intention. At last, the stage is set for a resolution.
In the Homeric world, the gods are constantly meddling in the lives of humans. Odysseus especially has many gods for and against him throughout his journey.
Most notable are Athena and Poseidon. Athena, the goddess of war and wisdom, is Odysseus's guardian and patron. She constantly tries to protect him and guide him. On the other hand, Poseidon holds a grudge against Odysseus for several reasons, mostly borne out of Odysseus's hubris. For instance, Odysseus blinded Poseidon's son, the Cyclops Polyphemus.
Athena and Poseidon have always had a kind of enmity between them. They often argue about different issues, and are nearly always on opposite sides of huge conflicts. This dates back to the founding of the city of Athens. The two gods fought over who would be the patron god of the city. They had a competition, which Athena won. (Thus, the name of the city!) Ever since, they have had a rocky relationship. Their respective feelings towards a human hero like Odysseus certainly affects the goings-on of the heavens.