Kalasin has its own Department of Land Transport that issues all driving licences for Thais and Foreigners. Go to reception and ask what they require or call 1584.
As a general rule you will need a Residency Certificate which you can obtain from Immigration there or at the Tourist Police Office, medical certificate that you can obtain for less than 500 baht on the day normally from around the corner and take your Australian Driving Licence and your Pink Card and Yellow Book. Definitely worth taking your wife also just to get through the grind of complexity..... But if you get stuck just call 1584 and someone should be able to help you in English or make it easier for your wife to speak to them.
Be prepared to go there more than once though as you may need to sit some tests or book an appointment online.
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