Why doesn’t Percy respond to his wife’s overtures? What do we learn about his motivation for treating her coldly? How does he truly feel about her?

They are very different:

Chauvelin, the novel's chief villain, is a French agent who has English diplomacy rights. He is in England looking for the Pimpernel and anyone else who is attempting to rescue French aristocrats. His 'hard-hearted, vengeful' nature contrasts with the dashing Pimpernel.

Lady Blakeney, while living in France as an actress, was famous for her beauty, but even more for her charisma, wit, and intelligence. When she marries Percy Blakeney, no one's quite sure what she's thinking. Since he's considered a dull turkey and she a renowned socialite, the consensus is that she's married down. But she discovers her husband's secret identity and we see her husband's heroism through her eyes.