The Mafia thing really does put emphasis on the family bonds that the Mafia liked to display when they wanted the public to forget about all the Mob War and killing they did. And it's still about family. Which is why it still reminds you of The Godfather. Don Lino positively adores both of his sons equally, even if one of them is a little embarrassing. Even when Lenny 'comes out', he blames Oscar, not him.
You do get that Frankie and Lenny are brothers and they love each other, even if they are different. Frankie tells his father he can handle the Reef, but that's not to steal it from Lenny; Lenny already doesn't want to and he's trying to take it off his shoulders.
"I love you son, no matter what you eat or how you dress." Hugs all around!
So for kids who don't get the metaphor for gay, there's a metaphor for cross-dressing, which is a more common joke in kid's films.