As Ken (hinted), just do it. You will need all the documents you supplied the first time + a letter "Responsability" from a resident. If you live in Santo Domingo, then go for it. I think you can deposit all your Docs. in Santiago but will probably have to go to the head office to pick up the card.
Depositing the documents in Santiago is a good idea, if they will accept them there. It is a relatively small office compared with Santo Domingo and better able to give some personal attention. If a lawyer were involved, he would be notified when process complete and,in turn, notify you. Your chances of getting the same sort of notification is better if you work through the Santiago office. When they receive word that approval has been given, they will contact you. Or, as time passes and you have heard nothing, you will have a contact in Santiago that you can call. But don't start calling immediately because nothing moves as fast here as you might like.
If I were doing the renewal myself, I would definitely try to work through the Santiago office.