Do I show USA Passport to verify ticket, then show Irish Passport to show I can get into Brazil without a Visa?
Exakt.
How does USA Airlines know that an Irish Passport does not need a Visa to enter Brazil?
TIMATIC-databasen.
Does Brazil see that I flew in from USA and booked ticket with USA passport?
Nej, de bryr sig inte heller. Du visar bara ditt (irländska) pass på brasiliansk gränskontroll ändå.