Prohibition of a    woman travelling without a mahram, and conditions of a mahram
Question

My mother is planning to go to ummrah inshallah. But she needs a mairram and her husband nor her brothers are able to go. We have asked an alm he said she can go with her brother in-law which is also her first cousin. As long as his wife is there which she will be cause she's going too. Is this permissable in Islam because I still have my doubts.
Praise be to Allah.One of the ways in which Islam protects women is that it requires a woman to travel with a mahram, to protect her from those who have bad intentions and to help her, because of her weakness, in facing the arduous trials of travelling. A woman is not permitted to travel without a mahram because of the hadith narrated by Ibn Abbaas (may Allah be pleased with him), who reported that the Prophet (peace and blessings of Allah be upon him) said: A woman should absolutely not travel unless she has a mahram with her. A man stood up and said, O Messenger of Allah, I have enlisted in such-and-such a military campaign, and my wife has set out for Hajj. He said, Go and do Hajj with your wife.(al-Bukhaari, al-Fath, 3006).
What indicates that a mahram is obligatory is the fact that the Prophet (peace and blessings of Allah be upon him) commanded this man to give up the idea of jihaad (on this occasion), even though he had enlisted for a campaign and his wife was travelling for the purpose of worship, not for some frivolous or suspicious reason. In spite of all this, he told him to go and do Hajj with his wife.
The ulamaa have listed five conditions for a person to be considered a mahram. He should be male, Muslim, adult, and of sound mind, and he should be a relative to whom marriage is permanently forbidden, such as a father, brother, paternal uncle, maternal uncle, father in law, mothers husband or brother through radaaah (breastfeeding), etc. (as opposed to relatives to whom marriage is temporarily forbidden, such as a sisters husband, paternal aunts husband, maternal aunts husband).
On this basis, the husbands brother and the son of a paternal or maternal uncle are not mahrams, so it is not permitted for her to travel with them.
And Allah knows best.