This is not an unusual problem in the Dominican Republic. Correcting the problem seems to be time consuming and expensive. My wife was born on March 17. Her Dominican birth certificate says March 7. One of my son's was born on December 30. His birth certificate says November 30. We investigated correcting the certificates and decided it was not worth the hassel.
Or, perhaps my wife decided it was not worth the hassel. She now expects birthday cards, flowers and presents on both March 7 and March 17.
Seriously, half the Dominicans that I know have errors on their birth certificates. Remember the little league baseball pitcher, Danny what's his name. His birth certificate, depending upon who you talk to, eather stated that he was born two years earlier or two years later.
In your case, if it were not so serious, it would be funny. Good luck on changing the "Acta de Naciamentio"