Is it permissible for the husband's brother to live with the couple in the same house if the Sharia-compliant regulations are observed and khalwa (private seclusion) is prevented, especially given the brother's need for care and the fear of him straying?

There is no objection to your brother living with you in the house if the Sharia-compliant controls can be observed, such as the absence of unlawful seclusion (khalwa) and impermissible mixing, and provided that your wife consents. If your brother occupies an independent section with its own facilities, so that your wife is not inconvenienced, then he may live with you without the condition of your wife's or her family's consent. Her family's objection is not to be heeded if it has no legitimate Sharia justification.