No. There are no mammals with more than one penis, though marsupials like koalas have a forked tip to the penis to match the internal anatomy of the female. Snakes and lizards have two separate penises, but I don't know of any animal that has three.
Did your mother get her doctorate in mammalogy? cetology? Did she even take a mammalogy course? All placental male mammals have a simple penis. Maybe she meant a three FOOT penis.
Just one
It doesn't matter how many penises whales have if they don't have any hands.
No.