If you are going to be doing business in the D.R., either personally or through a company, you will need to become a resident.
For the LLC to do business in the D.R. it's advisable that you go through the process of obtaining an authorized domicile ("domicilio autorizado") for the company. This process, however, requires a Presidential Decree which takes a long time. It's preferable (faster and cheaper) to form a Dominican company with the LLC as the controlling shareholder.