The Porcupine of Truth by Bill Konigsberg

New Yorker Carson Smith and  homeless Aisha Stinson meet at the Billings Zoo and strike up an immediate friendship.  Both teens are struggling to cope with their totally dysfunctional families, mainly with their fathers.  Carson's disappeared from his life when Carson was a young child and is now dying and Aisha's dad kicked her out because he cannot accept that she is gay.  The two of them decide to solve the mystery of Carson's grandfather, whom they suspect is still alive, although he deserted Carson's dad decades earlier. They embark on a cross country road trip which tests their ingenuity, their resilience, their sense of humor, and the strength of their relationship.