The visit of Odysseus to the Land of the Dead occurs in Book 11. It is of course important to realise that Odysseus confronts not only family members who have died, but also old friends and comrades-in-arms. Therefore, although the text does not explicitly indicate internal conflict, we can pick up that being confronted with family members such as his mother causes Odysseus considerable grief and mental hardship. Consider what Odysseus says about how he tried to embrace his mother after seeing her but was unable to:
Then I tried to find some way of embracing my mother's ghost. Thrice I sprang towards her and tried to clasp her in my arms, but each time she flitted from my embrace as it were a dream or phantom, and being touched to the quick I said to her, 'Mother, why do you not stay still when I would embrace you? If we could throw our arms around one another we might find sad comfort in the sharing of our sorrows even in the house of Hades; does Proserpine want to lay a still further load of grief upon me by mocking me with a phantom only?
Odysseus is clearly struggling with his sense of loss and grief and also he is finding it difficult to accept the finality of death. The phrase "sharing our sorrows" indicates that Odysseus, now that he is face to face with his mother, is able to express his true feelings of loss and desolation that he had been unable to before. However, because of the nature of death, he is unable to find physical comfort through seeing his mother. The internal conflict experienced by Odysseus is therefore best described as him trying to come to terms with the hardship that he has experienced and also accepting the terrible finality of death.