Or HaChaim on Genesis 43:8/אור החיים על בראשית מ״ג:ח׳

1 ונחיה ולא נמות, "so that we may live and not die." In order that we may live a life without anguish, or so that we may at least not die even if we have to live with anguish.

2Alternatively, the words ולא נמות were intended to tell his father that he could not claim that by not travelling to Egypt they would only find themselves deprived of life's comforts; rather, it would positively cause the death of their families. They would not even live a life of deprivations.

3Alternatively, Yehudah meant that if they would not now travel to Egypt with Benjamin they would eventually be called to answer for this in the Hereafter and would be guilty of not having made every effort to stay alive in this world.

4גם אנחנו, גם אתה, גם טפנו, "both we, and you, and our children." Yehudah referred to all the people whose lives depended on this trip in addition to Benjamin. If they did not travel with Benjamin, all of them including Benjamin were liable to die of starvation. All of this because of the possible danger to Benjamin in Egypt. It simply was not fair that they all should be condemned to death because of what might happen to Benjamin.

5The reason that Yehudah included Jacob's own survival last when he said גם אתה, was in line with the ruling that preservation of one's own life takes precedence even over saving one's father's life ( Yoreh Dey-ah 251). Or, the brothers used the exegetical rule of לא זו אף זו, "not only this but even this," i.e. the most important factor of the argument is presented last. They accorded their father the compliment of presenting preservation of his life as even more important than preservation of their own lives.

6According to this principle they mentioned their children last, as those represented the future and as such deserved the highest priority in their considerations (compare David rating Absalom's life as more important than his own even while Absalom sought to kill his father (Samuel II 19,1).