I don't think it's the baby, especially if she was asking on and off before you knew... but there is something about what you've written, I don't know, it makes me... uncomfortable. I could be reading too much into it, or it could just be the phrasing... I don't know.

How is her relationship with her dad? Could there be something going on there that makes her not want to live with him anymore but she wouldn't feel free to voice it in a group meeting about where she's going to live? Clash of personalities, girlfriends she doesn't like, neighbours giving her a hard time, something else again... It would be interesting to see what SHE would choose if you gave her the private option of living with you but having to go into care before and after school or staying with your XP - asking her at a time when you are alone with her (just the two of you), and she feels safe. If she was happy to go into an after school program instead of staying with her dad, alarm bells would be going off for me.