pronoun confusion

Lately, Dyami has been telling Lucy that she's his girl.

"Daddy my girl," Lucy told me today.
I did a double-take. "Your girl?"
"He my girl."
"Is Daddy a girl, Lucy?"
She laughed. "Nooooo," she said, with the tone, what, do you think I'm stupid?

Then, later at dinner with Daddy:
"Daddy, you my girl," she told him.
More double-takes. "Do you mean that you're my girl?" Dyami finally said.
"Huh, yeah," she said. "You my girl."
"No, if you want to say it, you'd say, "I'm your girl."
"You my girl."
"No, say, 'You my...'" He paused. "I mean..."

These pronouns, they're tricky.