I truly believe we should be more sensitive to what the brother is going through. I know that if my son (who is his age), was in this brother's position, he would be in an extreme state of panic and grief, tearing his hear out. Let’s not underestimate this issue.
There needs to be a balance between thinking of the mother and of the son. Focusing on one side only would be unfair. It is important that he is given guidance on how to approach the issue with his mother as best as he could because of a mother’s position in Islam, it's equally important that any criticisim is constructive and respectful.
He needs to gain the strength to deal with what he has, which is a very big issue that will test the strongest of people. He needs to Protect the boundaries of Allah swt at the same time keep within the boundaries of Islam towards his mother. The issue entails many challenges; some of which are his deen, his relationship with his mother, his manhood, accomodation to name a few..
Brother, make use of phone calls to sheikhs rather than visits, to reserve privacy re topic . Also, depending on your relationship with your mother, and how difficult it is to speak 1:1, you could consider emailing her your stance, feelings and islamic viewpoint , provide links of videos regarding topic. Watch them first and be selective as to what you think would have a better impact inshallah.
Moving out needs to be weighed up.
Advantages could be that if you have a valued position in the family, then your mother could feel the loss and think about how she is driving you away.
Disadvantage/s are if shaitan is too strong to make her realise that, and if your siblings don't share your stance on topic, then then leaving could mean that matters continue. In this instance your presence could prove vital to protect your family. Do istikhara and consult a sheikh.
May Allah be with you. Remember we are tested in life in all sorts of ways, and this happens to be one of them for you. Sometimes we are tested withthe closest people to us. Our parents can be our tests too! Ibrahim PBUH was tested with his father Azar, Noah with his son, Asia R.a with husband pharoun, Lut PBUH with his wife. it's worth looking into how they met these calamities and following their examples.
Al-Tirmidhi (2398) narrated that Sa’d ibn Abi Waqqaas (may Allaah be pleased with him) said: I said: “O Messenger of Allaah, which of the people are most sorely tested?” He said: “The Prophets, then the next best and the next best. A man will be tested in accordance with his level of religious commitment. If his religious commitment is strong, he will be tested more severely, and if his religious commitment is weak, he will be tested in accordance with his religious commitment. Calamity will keep befalling a person until he walks on the earth with no sin on him.” Classed assaheeh by al-Albaani in al-Silsilah al-Saheehah, 143.
As tough as this is, try and deal with it the best way and you will be getting reward from Allah SWT To help you do that seek scholarly advice so you know you are on the right path inshallah and not get too confused with all the opinions. Make dua for Allah swt to change this situation.
The Prophet PBUH expressed this in a saheeh hadeeth in which he said: “How wonderful is the situation of the believer, for all his affairs are good. If something good happens to him, he gives thanks for it and that is good for him; if something bad happens to him, he bears it with patience, and that is good for him. This does not apply to anyone but the believer.” (Narrated by Muslim, no. 2999).