you are correct Dave and yes you need your passport translated into Thai as well. The district office will issue a marriage certificate in Thai and a Kor ror 2 document. These can used to obtain a visa based on marriage to stay in Thailand 🇹ðŸ‡
After the above procedure once your in Thailand have your certified marriage certificate translated into Thai by somebody who is recognised by the ministry of foreign affairs as certified to translate. Then simply visit your local Amphur 'district' office they will issue a certificate in Thai and a Kor ror 2 document.