I have a feeling she's learned to be independent. Nanako's over-maturity simply highlights the ineptitude of Dojima's parenting. He can't hardly do any domestic tasks, which is probably a portrayal of Japan's more traditional gender roles. I doubt he had the need to do any serious housework. The death of his wife probably took the family into a tailspin. Not to mention the social pressure of a lone dad raising a child. Single-mother households are a rarity (though increasing, slowly), so single-father households are even more so. That and he has a hard job; I'm surprised he manages.

Really though, Nanako only becomes sweet after a month of getting to know you. She was always polite, but she was fairly shy around you until about Golden Week. Her exuberance towards Yu and his friends is probably a reaction to the lack interaction she had before he turned up. It sounds almost tragic, but her life was basically school -> housework -> T.V -> repeat. Someone wants to spend time with me?! If you were seven and had stunted social interaction, you'd be more than little 'eager'. Her contentment with otherwise small occasional trip is probably again an over-reaction; of getting as much joy as you can from it because you don't know when the next will turn up.