Is buying a car by taking a loan from the bank with the mother's account as collateral, and repaying it with specified interest while freezing the guaranteed amount from the mother's account, permissible or forbidden (halal or haram)?

The reality of a loan is taking money and returning its equivalent. Any stipulated increase on it is considered usury (riba), which is Haram (forbidden) by consensus, whether the increase is in kind or benefit. Therefore, it is not permissible to enter into a loan transaction with interest with the bank, even if the bank freezes a portion of the mother's account, because the usurious transaction has already occurred between the borrower and the bank.