Should he obey his mother by taking out a riba-based loan?

Praise be to Allah.

Firstly: 

It is obligatory to obey parents except in matters that are sinful, because the Prophet (blessings and peace of Allah be upon him) said: “There is no obedience to any human being if it involves sin; obedience is only in that which is right and proper.”

Narrated by al-Bukhaari, 7257; Muslim, 1840.

And he said: “There is no obedience to any human being if it involves disobedience of Allah.”

Narrated by Ahmad, 1098 

Obedience to parents is obligatory upon the child in matters that are beneficial to them and do not harm the child. With regard to that in which there is no benefit for them or there is harm for the child, he is not obliged to obey them in that case. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said in al-Ikhtiyaaraat (p. 114): The individual is obliged to obey his parents in matters that are not sinful, even if they are evildoers. … This has to do with that which is beneficial for them and not harmful for him. End quote. 

Secondly: 

With regard to what your mother said about it being obligatory for you to obey her, that is true and it is enjoined by Allah, may He be exalted. But if there is a conflict between the command of Allah, may He be exalted, and the command of the mother or father in that they command you to do something that is contrary to the command of Allah, the believer has no doubt that what he should do is give precedence to the command of Allah, may He be exalted. Hence the Prophet (blessings and peace of Allah be upon him said:

“There is no obedience to any human being if it involves sin; obedience is only in that which is right and proper.”

Narrated by al-Bukhaari, 6830; Muslim, 1840. 

It says in al-Mawsoo‘ah al-Fiqhiyyah, 28/327 

Obedience to other people – those to whom obedience is obligatory – such as parents, the husband and those in authority – is restricted to matters that do not involve disobedience or sin, because there is no obedience to any human being if it involves disobedience of the Creator. End quote. 

Shaykh al-Fawzaan (may Allah preserve him) said: 

Women are enjoined to obey Allah, may He be glorified and exalted, and they are enjoined to obey their husbands and parents, within the framework of obedience to Allah. 

But if obeying a person such as one’s father or husband involves disobedience of the Creator, this is not permissible, because the Prophet (blessings and peace of Allah be upon him) said: “Obedience is only in that which is right and proper)” (narrated by al-Bukhaari) and he (blessings and peace of Allah be upon him) said: “There is no obedience to any created being if it involves disobedience to the Creator” (narrated by Ahmad). End quote. 

Al-Muntaqa min Fataawa al-Shaykh al-Fawzaan, 1/265, 266, Question no. 161 

Based on that, it is haraam for you to take out a riba-based loan in order to buy a house – as you know, may Allah bless you – so you should let your mother know that it is haraam for you to obey her in that, and that her anger with you is as nothing before Allah, may He be exalted. But you should treat her kindly because of the great rights that she has and her status before Allah. 

You have to be gentle with her and try to convince her that no matter how much you may gain from something haraam, there is no barakah in it and it will lead to bad consequences.  

We ask Allah to make good easy for you where ever you are. 

And Allah knows best.