Your fiancé would have the best knowledge on how to obtain that from her local amphur. After she obtains her birth certificate she can have it translated in Bangkok.
Can get translated in Bangkok but you’d have to use the amphur near her village in Roi Et. Not sure if you’ve heard about it but visajourney.com is quite helpful. 
I’ve known two Thai women that were previously married to Black American men. They didn’t have anything negative to say any differently from other couples that split up.
I’m not sure how it will/should work for you but I’ve (US passport) only ever gotten my police check in Bangkok. Takes about two weeks now if I remember correctly.