Before you get too wrapped up with how many DC's are needed and whether or not they're needed in remote locations, take a look at the bigger picture:
Are there local resources (Exchange, file and print, etc.) at each remote location that users need to authenticate to the domain in order to access?
If the answer is yes then it behooves you to place at least one DC in each remote location so that in the event that the network connection is down users will still be able to authenticate to the domain and access those local resources.
If the answer is no, then having a DC at each remote location is pointless as the users won't have access to the main office resources if the network is down. Being able to log on to the domain via the local DC does them no good. Users will be able to log on with cached domain credentials, possibly browse the internet (depending on the nature of the network problem and on which side it is occurring) but that's about it. So what good will having a local DC do?