If you go 60 days visa exempt, then extend with 30 days for 1900 Baht at Immigration office, before you travel out of Thailand, to get a new visa exempt period.
Apply from your country or the country you are in right now, then you don't have to go any other country, but can go direct to Thailand.
It may be easier to get documents approved in the country where they are issued, and the Embassy is use to see those documents.
You may have to get your own DTV before you can apply for the dependants, and of course you have to pay visafee for everybody, since the Embassy have to do the same work to proces every application.