Ya i dont think there was ever a reference to carmine being a captain, all it was said about him was he was fixing wet tshirt contests. Little carmine was just rusty millios little puppet and carmine thought he was entitled to it bc he was his fathers son, i guess he watched the godfather to many times where micheal succeeds his father even though hes in no way qualified.

"Let me tell you something. There's no nobility in poverty. I've been a poor man, and I've been a rich man. And I choose rich every fucking time."

-Jordan Belfort