Indeed, Frank's actions can be seen as an abandonment of his family. I think that he justifies this in a couple of ways. The first is that Frank recognizes that staying in Ireland is going to result in nothing more than the same miseries and the same impoverished conditions:
Mam turns toward the dead ashes in the fire and sucks at the last bit of goodness in the Woodbine butt caught between the brown thumb and the burnt middle finger. Michael . . . wants to know if we’re having fish and chips tonight because he’s hungry. Mam says, Next week, love, and he goes back out to play in the lane.
Unlike his brother, Frank understands the reality of the situation. He understands that reality in Ireland, the true pain of poverty is the denial of transformative dreams. Frank justifies needing to leave and thus abandon his family in order to pursue dreams and embrace the quality of what can be as opposed to what is. For Frank, this becomes part of his rationale in leaving. It makes sense that he sees his departure in a dream:
I’m on deck the dawn we sail into New York. I’m sure I’m in a film, that it will end and lights will come up in the Lyric Cinema. . . . Rich Americans in top hats white ties and tails must be going home to bed with the gorgeous women with white teeth. The rest are going to work in warm comfortable offices and no one has a care in the world.
In order for Frank to escape the blight of poverty in Ireland and the condition that denies hope in dreams, Frank sees himself as needing to leave. His abandonment of his family is the price he pays for a reality where "no one has a care in the world."
Interestingly enough, I think that a case can be made that Frank justifies leaving his family because of religion. When Frank confesses his sins regarding Teresa to the priest, he begins to understand that religion does not have to be a force of oppression and pure guilt. Frank interprets his confessional talk with the priest to be one that "tells me God forgives me and I must forgive myself, that God loves me and I must love myself for only when you love God in yourself can you love all God's creatures." This benevolent love is in contrast to the harshness and disappointment with which he has viewed all authority figures in his life. Institutional repression in the form of schooling and lack of occupational opportunities and personal failures such as his father and the guilt from traditional Catholicism have contributed to Frank not believing in much regarding redemption. "Fear not said the voice" is what Frank gains regarding religion. This aspect of spiritual identity allows Frank to be free of guilt. It might be this idea which helped Frank to move towards a transformative vision of consciousness in the world, enabling him to leave and abandon his family.