Do the actions of a husband who abandons his wife and children, leaves them without financial support, and treats her poorly, please Allah and His Messenger? What is the ruling on a husband who abandons his wife without a legitimate Sharia reason? And what should the wife do if he persists in this condition?

The husband mentioned in the question is disobedient to Allah and His Messenger, and unjust to his family. His neglect of his children, abandonment of his wife, and accusing her of wrongdoing without proof are actions that should not emanate from a husband, and he incurs sin for these behaviors.

The wife should be patient and supplicate for her husband's guidance. If his situation does not change, she can seek help from someone her husband trusts to advise him. If he does not respond, she has the right to seek divorce due to harm, or to be patient to preserve the family.

Moreover, the ruling on combining the wife and the husband's son from another marriage in one dwelling, and the detailed juristic opinions on it, are mentioned in Fatwa (definition) no. 74359.