Where in Hat Yai or elsewhere in Thailand can a person get his Thai car registration translated to English so that he may drive his Thai registered car from Thailand to Malaysia?

Take your car documents and your own photo ID (Passport) to the local Land Transport Office. Ask for a translation. Once you have this official form you can take it to one of the many vinyl printing shops and get a couple of self-adhesive stickers made to adhere to the vehicle front and rear.

Land Transport Office for HatYai is on Phetchakasem Road. (From Carrefour head out of town on Phetchakasem Road and the Office is on the RHS before you arrive at the next set of Traffic Lights. There is a sign on the building at the front saying in English "Drive through Tax" or something similar. The building you want is behind that one, maybe on the 2nd floor from memory!)

Hope that helps.