if two ADR disagree, as it was the case for the Air Caraïbe and the AF 447 flights, normal law should irreversibly switch to alternate law 2, if one ADR fails, it switches to alternate law 1 with possibility to revert to the normal law, as it was the was for the Qantas flight, 3 seconds after the 2nd pitch down.
this does not explain to me why a faulty ADR (how could it detect itself that it is generating erroneous measures ?) give rise to an IR failure when nothing anomalous is seen with it (does the post flight analysis show any defect with the IRU part ?). but this is nother problem.
it simply suggests that faulty/disagreeing ADRs can trigger IRU fault reports and alternate law 2 (plus a strange behaviour of the autopilot)
Jeff