Ulysses is conflicted because he feels the obligation to be with his family but he also feels the urge for adventure. So, Tennyson presents Ulysses as someone whose main desire is adventure. And since the adventures that he craves are dangerous, Ulysses is described as a frustrated king, anxious to journey and commit to adventures that would necessarily require a heroic man to attempt them. Ulysses is admirable because it is easy to admire one, especially in his relatively old age, to continue to strive to live life to the fullest. But Ulysses is selfish in this respect as well. He is willing to leave his wife in order to make at least one last journey.
That being said, it is not that Ulysses does not care for his wife (although he notes his boredom being "Matched with an aged wife"). Ulysses simply feels that life is worthless unless he makes the most of his time. It means nothing to him to sit and govern as king. To be so complacent is, to Ulysses, to waste away and wait for death.
How dull it is to pause, to make an end,
To rust unburnished, not to shine in use!
Ulysses reasons that his son is more suited to sit as a king. In the context of the poem, Ulysses shows himself to be a reluctant (or maybe even irresponsible) king and an unsatisfied husband. But he also shows himself to be an indomitable spirit.
Despite this conflict of selfishness and heroism, one can read the poem for its broader themes of never becoming complacent, of living life to the fullest until the very end, "To strive, to seek, to find, and not to yield."