What is the ruling of Islamic law concerning a wife who denies her husband his marital rights, abandons him, incites their children to hate their father, and takes his money without his knowledge, despite his fulfilling all her demands?

The Sharia has granted men qawamah (guardianship/headship) over women and obligated wives to obey their husbands in what is good, which includes responding to his call for intimacy. If a wife refuses without a legitimate Sharia excuse, she is sinful and nashiz (rebellious), and the husband is permitted to discipline her as stated in the verse: "Men are in charge of women by [right of] what Allah has given some over others and what they spend [to support them] from their wealth. So righteous women are devoutly obedient, guarding in [the husband's] absence what Allah would have them guard. But those [wives] from whom you fear defiance - [first] advise them; then, if they persist, forsake them in bed; and [finally], strike them. But if they obey you [thereafter], seek no means of [annoyance] against them. Indeed, Allah is ever Exalted and Grand." It is advisable to supplicate for her righteousness and to be patient with her if there is benefit in doing so.