Legal Question in Civil Litigation in California

Your question does not make sense. You cannot litigate the same claim in multiple courts, much less multiple states. If there are separate claims in three different states they are separate claims no matter how similar or related, and the duty to defend is determined on each claim separately. A decision on a duty to defend a California claim is entitled to full faith and credit in other states, technically, but that is not really relevant at all, because that case must be defended in California. So no other state's courts would ever be called upon to have anything to do with that decision, and that decision would be irrelevant to deciding if there is a duty to defend some other case in another state, since the case in another state would not be the case the California court says there is a duty to defend.

Yes, the order would be entitled to full faith and credit by courts in other states. As Mr. McCormick suggests, however, this may not mean very much. It will all depend on your circumstances.