While doing some research on Princess Mononoke, I came across an interview with Hayo Miyazaki about the film and his thoughts on some of the characters, including Lady Eboshi.
The interview has been translated on a Studio Ghibli fan site here: http://www.nausicaa.net/miyazaki/interviews/m_on_mh.html
In the interview, he talks about Eboshi’s back story.
“I thought up a story that she was a wife of a Wako boss (Japanese pirates/smugglers who raided the Chinese and Korean coastlines)”
“What Eboshi is trying to do is to build a paradise as she thinks of it.”
He infers that establishing Iron Town is a reaction to her previous life as a smuggler’s wife. This could be because she was abused, explaining her sympathy and respect for the sex workers that she’s employed and empowered in Iron Town. However this doesn’t account for her sympathy for the leppers. Perhaps she’s just an accepting person with a place in her heart for the outcasts of society?
Although she’s a wise and reserved character, she has a lot of hate inside her that she takes out on the forest; A profitable use of her demons. Perhaps this back story is the source of her un-wavering drive?