Pellegrina is currently a frazione (village) within the town of Bagnara Calabra although it appears to have been a separate town before 1866.
Many records for Bagnara Calabra are online. The following is the death act for Vincenzo and Maria's son Giuseppe.
Click on image to enlarge.
Births are only available from 1866 to 1900; the key document you need is Vincenzo's birth act from 1912 which will give his birth date, parents' names including mother's maiden name, their ages and occupation.
Then you can work backwards to locate the parents' birth acts and marriage act and continue to work backwards. Usually the first son was named after his paternal grandfather; if Vincenzo and Maria followed this practice Vincenzo's father would have been Giuseppe. Again, Vincenzo's birth act will give you this information. Unless you have other documentation you should write to the Stato Civile office in Bagnara Calabra to request a copy of Vincenzo's birth act. Let me know if you'd like to do that and I'll help you put together a letter to request it; if you know his wife's birthdate you could also request a copy of her birth act as well as a copy of their marriage act since they married in Italy.
Here's a link to the full listing of Bagnara Calabra records which are available online. Nati--Births; Morti--Deaths; Matrimoni--Marriages.
And one for Pellegrina for records before 1866.
None of the above records are indexed but each year usually will have an alphabetical yearly index at the end of the year with the act number.
A couple of places for help learning how to extract records.
This one is very helpful in learning how to translate dates, months, years, ages, occupations, etc.