All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If your wife had really called the police on you and she had no sound reason for doing so, like in order to repel your harm from her and the like, then she is undoubtedly wrong and this act is considered a disobedience on her part. Likewise, she is wrong for driving you out of the house. However, you should have tried to solve the problem by seeking the help of your Muslim brothers there before going back to your country.
As regards spending on this girl, it is an obligation on you if she has no money that her mother could spend on her. If her mother spends on her and she wants to ask you to reimburse her for that, then she is entitled to do so.
With regard to your statement that your wife is no longer a Muslim, if you mean that she apostated, then your marriage to her is invalidated. If she re-embraces Islam before the end of her waiting period, then she is still your wife with the first marriage contract. However, if she continued on her apostasy until her waiting period expired, then she would no longer be your wife. Allaah Says (what means): {And hold not to marriage bonds with disbelieving women.}[Quran 60:10] For more benefit, please refer to Fataawa 105332 and 106948.
Moreover, you should know that an apostate woman has no right in the fostering of the children, so if your wife continues to be an apostate, then she has no right in fostering this girl, so you should seek a way to take your daughter from her.
Finally, it should be noted that it is not permissible for a husband to accuse his wife of having an affectionate relationship with another man without evidence; Allaah Says (what means): {O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin}[Quran 42:12]
Allaah Knows best.