I have not seen that movie, but I would assume that in that scene they were trying to portray the character as being humorously incorrect.
I think that "Dool-CHEE-nee-uh" would be the sort of pronunciation someone who was familiar with Italian names but not Spanish ones would try to use. "dool-sin-AY-uh" would be closer to the original Spanish pronunciation, and
Don Quixote is originally a Spanish novel, not an Italian one.