Is it permissible to seek divorce from a husband who does not provide for his wife, harbors ill-suspicion towards her, and suffers from Alzheimer's disease, given that the wife has no place to live after divorce?

If a husband does not provide for his wife adequately, she is permitted to take from his money without his knowledge what suffices for her maintenance, based on the Prophet's (peace be upon him) saying to Hind: "Take what suffices you and your child, according to what is reasonable." If she is unable to do so, she may refer her case to the judiciary.