Yes, to redeem his family's honor, but also, imho, to guarantee the safety of his brother.
Actually he guaranteed the safety and honor of his brother the moment he changed his testimony at the hearings.
The meeting with Hagen was to save HIS honor and to make sure that his family would be taken care of for life.
And if he didn't kill himself, do you believe that his brother would not have been bothered?
I really do. I believe that once Frankie recanted his earlier testimony, his brother's honor and safety had been restored. Tom even turns to him and tells him in italian that his (Vincenzo's) family's honor is ok.
Don Cardi
Five - ten years from now, they're gonna wish there was American Cosa Nostra. Five - ten years from now, they're gonna miss John Gotti.