The Unlikely Earl by Lorea Hartwell

When Miss Sophia Lightbourne’s spoiled sister runs away from home, there’s only one thing Sophia can do: follow her to London to try to save Kitty from being ruined.
Problem number one: Kitty doesn’t seem to care if she’s ruined.
Problem number two: Augustus Alleyne, the strugglng portrait painter whose help Sophia needs. Yes, he’s handsome and witty… but she very much suspects that he’s a rake!
Yet as they follow the trail of destruction and broken hearts left by the heedless Kitty, their connection grows passionate. Does what happens in London stay in London? Sophia tells herself that it does. But her heart is telling her otherwise. Saving Kitty is getting more complicated by the day… especially when Alleyne makes Sophia want to fall into ruin herself.