The Duchessa smiled reprovingly and shook her head when she went away.

It would have been quite impossible for her to explain to Veronica why she should not remain longer than necessary under Bianca's roof.
And, indeed, the matter might not have been easy to explain.

Veronica was glad when she was gone.
The cardinal was not so easy to deal with.

He was a man of singular intensity of opinion, so to speak, when he held any fixed opinion at all, and he was displeased when he learned that Veronica was with his niece.

On the other hand, the fact that Bianca was his brother's daughter gave Veronica a weapon against him.