As Pete astutely pointed out: Frankie was already wavering about his testimony before Vincenzo appeared:
Sure thing Frankie was wavering
Mort' -- my life -- my life won't be worth a nickel after tomorrow!
As regards
“and his enemies would stop at nothing to get rid of him, even, as LucaB said, kidnapping or killing his grandchildren”
Mafia's code of conduct and ethics! – No kidnapping or killing of women and children
