"Dulce" is a PORTUGUESE female first name and means "sweet". It is my first name and I'm Portuguese, not Spanish.
It also has the meaning of "sweet" in Spanish and is part of a few PORTUGUESE words like "dulcissimo" (very sweet), "dulcificar" (make sweet), "dulcineia" (girl friend); every word in Portuguese starting with "dulci-" has a meaning relating to "sweet".
Please bear in mind that the Spanish and the Portuguese languages are not the same, though they both come from Latin, of course.
As for every Latin language, there were two ways words entered the newly-formed languages: thru the common people (with less or no education, as Roman soldiers) and thru the cultivated people (at the time, essentially monks and similar people who received some education) - words in Portuguese starting with "dulci-" came thru the latter.
P.S. By the way, do you know where the name "Rodrigues" comes from? I'll tell you next time