Is it permissible to give the wife a monthly sum for her to save in an interest-bearing bank account, despite the husband's objection to that?

If the husband provides his wife with food, clothing, and shelter commensurate with his financial ability, he is not obligated to give her additional pocket money. It is not permissible for a Muslim to deal with usurious banks, nor even to open a current account with them, unless there is an urgent necessity. Therefore, it is not permissible for you to give your wife money to open an account in a usurious bank.