Is it permissible to take out a loan from an interest-based bank to purchase a home, in order to avert psychological harm to children caused by cramped living conditions and their exposure to parental privacy?

Usurious transactions are not permissible except out of necessity and commensurate with that necessity, as Allah the Almighty says: "unless you are compelled to it." So, if you are unable to rent accommodation that suits your needs and the needs of your family except with unbearable hardship, then there is no harm in taking a usurious loan to meet this necessity, if you cannot find a permissible alternative such as an interest-free loan (Qard Hasan (definition)) or a permissible transaction like Tawarruq.