Just like Stuart says. When you reenter Thailand with a reentry stamp Day 1 starts all over again. BUT you have to report to immigration office within 24 hours of your arrival. Then you will get paper in your passport with the new 90 day report date.
I got a new passport at the Belgium embassy in Bangkok. They also gave me a letter to give to Thai immigration explaining the reason for the issuance of a new passport. Take your old and new passport to immigration and they will transfer everything to your new passport.
The passport you arrive in Thailand with is the one you will use when you go somewhere that your passport is required. Such as immigration. You cannot use the other passport that does not have an entry stamp and
The International Drivers License is not really a license to drive at all. It is accepted in participating countries and is meant for temporary use only along with the license from your country. If you are planning to be in a country for a long period of time then you are required to get a driving license from that country. The worst case is you are involve in an accident possibly people are fatally injured and you do not have a driving license from that country. Your insurance company will refuse to pay any claims either repairs or medical expenses. If the accident is your fault the other parties will be taking you to court for damages and medical cost. With this in mind go get a driving license from the country you are living. In Thailand the process is easy if you original driving license is in English The previous comment is although true is not very good advice and irresponsible.