What is the ruling regarding the wife remaining in suspension, with the husband unwilling to divorce her or provide a home for her and their daughter, and what is the ruling regarding the maintenance from his wealth, and what is the ruling on taking half of the house?

If what you have mentioned about your husband is true, then he is at fault in two ways: his sheltering of a foreign woman in his house, and his abandonment of you and your child and his striking of you. If the matter has reached the point of ill-treatment, then separation is better, and he must agree to divorce you without requesting any financial compensation if he is the one who caused harm. Khul' (divorce at the wife's instance) in exchange for relinquishing custody is permissible, but the basic principle is to consider the best interest of the child. So, do not relinquish custody of your daughter if she would be harmed by staying with him. As long as you are his wife, you are entitled to maintenance and lodging in a reasonable manner from him, and he is responsible for the maintenance of his daughter. It is not permissible to resort to man-made courts except out of necessity, nor to act upon their rulings that contradict Islamic law. We advise seeking assistance from Islamic centers and the Muslim community to resolve the issue away from man-made laws.