I'm studying English fiction and don't understand the statement below (which I've put in bold), which I found reading a short story written about 50 years ago by an English author: Till September Petronella by Jean Rhys.
"You’re mean," she said to Julian, "and you hate girls really. Don’t imagine I don’t see through you. You’re trying to get me down. But you won’t do it. If you think you’re the only man in the world who’s fond of me or that I’m a goddamned fool, you’re making the hell of a big mistake, you and your mother."
She plucked a hairpin from her hair, bent it into the shape of pince-nez and went on in a mincing voice "Do Ay understend you tew say thet may sonn—" she placed the pince-nez on her nose and looked over it sourly "—with one connection–"
"Damn you," said Julian, "damn you, damn you."
Context: A young woman is arguing with a man (her close friend) and mocks his mother, who belongs to upper class and lives in countryside. Settings: 1914, somewhere near London.
Can this be read "Do I understand you to say that my son -- with one connection --"? Though it's not a complete sentence, what does this statement seem to mean?