All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible for your father to perform Hajj at the expense of your brother if the latter agrees to spend on his Hajj. Indeed, he will get a great reward by doing so as this is considered as being kind and dutiful to the father and keeping good ties with him. For more benefit, please refer to Fataawa 155281 and 89913.
On the whole, it is permissible for a Muslim to perform Hajj with the money donated to him by others even though the scholars differed in opinion whether or not he has to perform Hajj if others give him what he needs to spend on his Hajj. The most preponderant opinion is that he is not obliged to perform Hajj with this money, but it is permissible for him to do so and his Hajj is valid. However, if it is his son who gives him the money, then he is considered as being able to perform Hajj and he is obliged to perform it in case he did not perform his obligatory Hajj before.
In case the bank loan that you mentioned is from a usurious bank, then, initially, it is not permissible for you to take this loan and it is an obligation to repent from it if you have already taken it. In this case, you are obliged to only give back the capital money without any interest, and you should not pay it unless you are obliged to do so. For more benefit, please refer to Fatwa 86136.
Allaah Knows best.