Is it permissible for a father who has not provided for his daughter since her birth, has not inquired about her, lives in another country, and is married to a non-Muslim woman, to take his daughter from her mother, who is married to another man?

It is permissible for the father to take his daughter, provided he is obligated to pay her expenses for the past years to whoever spent on her, because the mother's custody rights are forfeited upon her marriage. This is unless it is proven that the father is unfit for custody, in which case custody transfers to the next in line after the father. The ruling in such cases is referred to the Sharia court, or to the Muslim community, consisting of scholars and dignitaries, if a court is not available.