Is it permissible to take bank interest money and give it to needy relatives, knowing that this money is designated for buying a house for the mother and there is difficulty in providing assistance due to the mother's treatment requirements and delayed marriage?

It is not permissible to deal with a bank by depositing money in it, unless you are compelled to do so for fear of theft and cannot find an Islamic bank. In such a case, it is permissible to place it in a current account without interest. However, since you have already done so, you must repent, withdraw the money, and place it with a trustworthy entity that does not deal with usury. You must also dispose of the usurious interest by giving it to the poor and needy, such as maternal uncles and aunts, with the intention of divesting yourself of it, not as charity.