It sounds like your ex-husband knows that he is not the biological father of your daughter, but has chosen to take her in anyway. His attitude is most commendable. Even though he is not your daughter's biological father, he is still her mahram provided he had sexual intercourse with you. Thus, it is impermissible for him to marry her and he must treat her as if she is his daughter.
It is not unlawful for your daughter to live with her stepfather and half siblings. However, once your ex-husband re-married, please think of your daughter's well-being. She may be far better off living with you, and visiting her stepfather from time to time. I would definitely suggest that she come to live with you by the time she enters puberty. At the same time, if your ex-husband is the only father she has ever known, it may be wise to encourage her to maintain ties with him, provided that Islamic decorum is observed.