the problem is that there is no "v" in arabic. at least not standard arabic (maybe they had it in andolusi arabic back in the day). so i guessed that the "v" was a corrupted "b" (ب) or it could be a "w" (و).
they both work--that is, an arabic word exists if you go either way with the "v." assuming the "v" is a "b" the original word could be "al-mudabbir" (المدبر), which means "the manager," "the leader," "the ruler," etc. so maybe one of pedro's ancestors was an arab leader.
if, on the other hand, the "v" is really a "w", you get "al-mudawwar" (المدور), "the round." at first that seemed to be less likely (maybe pedro's ancestor was really fat?), but then i found this:
Castillo de Almodóvar del Rioso now my best guess it that pedro's ancestor was from this castle, or, at least, took the name of the castle as his last name.
The name Almodóvar comes from the Arabic word al-Mudawwar, which means 'the round', a reference to the hill on which this castle has been built. The castle was built in the 14th century in Gothic style and has been considered as one of the most important castles in Andalusia because of its beauty and perfect condition. From the castle there is a fine view of the countryside of Córdoba.