The Duke says how he didn’t have the speech skills to confront her about his problem and if he did she would probably make an excuse to get out of being “lessoned.”
Even if he was a skilled speaker, he didn’t want to talk to her because that would be stooping to her level and he thinks he’s above his wife.
The Duchess smiled at the Duke when she would pass him, but why would it matter if she smiled like that at everything.
The said how the aforementioned grew. I assume she would keep smiling at everything and the Duke couldn’t take it.
“Then all smiles stopped together. There she stands as if alive.” Presumably the Duke either killed her, sent her away, or she just died of natural causes (stopped together as in the Duke and Duchess stopped smiling).
The Duke tells the servant to stand and come with him to talk to the other company. The Duke telling the servant to stand is almost like a command like before.
The servant is revealed as the servant of a Count who has a daughter the Dukes wants to marry.
The Duke wants a large sum of money as a dowry from the generous Count.
The Duke shows the servant his bronze statue of Neptune taming a seahorse, seahorses can be a symbol of generosity and sharing.