In all likelihood, there is very little that you can do in this situation against the police. First of all, the police in Idaho will have a limited immunity and even if they don’t, under Idaho law, they can rely on the information which the Washington DOL puts in the computer system. If the Idaho police relied on this albeit false information to make your arrest, then you cannot sue them due to negligence. On the other hand, if the Washington DOL negligently failed to list you as being reinstated, you might be able to sue them. This beings with the filing of a tort claim against the sate for your financial losses you suffered as a result of being arrested. Ultimately this comes down to proof. And you’re correct in that you need to focus your efforts on choosing the right lawyer. Look for one who has experience in filing tort claims against the state. You may also find lawyers willing to help you who have experience in personal injury or civil rights litigation. Again, I don’t think there’s anything else you can do against the State of Idaho, so look for a Washington lawyer to serve your interests.
The government is generally immune from civil tort claims. Even if there is a valid case, there is often a cap on how much you can collect, and lengthy time limits on how much notice the government needs to be given.
Contact a local lawyer that does civil rights violations.