I don't think that Elizabeth was influenced in her way of life. I think she chose that way of life as surely as Sir Walter did. And for the same reasons. She was with Lady Elliot even longer than Anne, so if there was one daughter who had the chance of being like her mother, you would think that Elizabeth had the best chance. And she's probably the least like her (as far as we can tell from what little we're told about her). Which is why I think Elizabeth chooses to live the way her father lives with enjoyment and passion.