Is Brother-in-Law Mahram?
Question

1. What is the position of a woman when her husband invites his brother to dinner, does she eat dinner with them, can she serve him?
2. Is the husband’s brother a mahram, can she travel with him?
Praise be to Allah.Can your wife serve your guests?
A wife is permitted to serve her husband and his guests if she is wearing complete hijab and nothing of her body can be seen. She is also permitted to sit with them so long as there is no sitting alone with one non-mahram man, wanton display or other cause of temptation involved.

As far as eating with them is concerned, if this involves uncovering some part of her body, then she should not eat with them.
Is a brother-in-law a mahram?
The husband's brother is not a mahram . The various types of mahram have been described in the Quran. On this basis, it is not permitted for her to travel with him .

In view of the seriousness of the matter of non-mahram men, especially the husband's relatives, entering upon women , and the fact that so many people take this matter lightly, there follow a few words of important advice:
Warning against non-mahram relatives entering upon women in the absence of their husbands
Some homes are not free of the presence of relatives of the husband who are not mahrams of his wife. They may be living with him for a number of reasons, such as brothers who are students or bachelors. These men enter the house without there being any sense of something strange, because they are known to the neighbours as relatives of the head of the household. The neighbours know that this is a brother, or nephew or uncle. This casual approach leads to many immoral deeds that earn the wrath of Allah because the limits that He has prescribed are not being adhered to. The basic principle in this matter should be the hadith of the Prophet (peace and blessings of Allah be upon him): "Beware of entering upon women." A man of the Ansar asked, "O Messenger of Allah, what do you think about the brother-in-law?" He said, "The brother-in-law is death." (Reported by al-Bukhari, Fath al-Bari, 9/330)

Al-Nawawi, may Allah have mercy on him, said: 
“This hadith refers to all the relatives of the husband apart from his father and sons, who are mahrams for the wife and she is allowed to be alone with them; they are not described as "death." It refers to the brother, nephew, uncle, cousin and other relatives of the husband whom she would be permitted to marry if she were not already married. Because people customarily treat this matter so lightly, and a man may sit alone with his brother's wife, the brother-in-law is likened to death, and he is the foremost among non-mahram men who should be prevented from doing so.
Meaning of ‘the brother-in-law is death’
The expression "the brother-in-law is death " may have a number of meanings, such as the following:

That being alone with a brother-in-law may lead to religious doom if it results in sin.
That it may lead to actual death if an immoral deed is committed that dictates the punishment of stoning.
That it may spell disaster for the woman if her husband's jealousy leads to divorce.
That you should fear being alone with a non-mahram woman as much as you fear death.
That being alone with a non-mahram woman is as terrible as death.

All of this stems from the fact that Islam wants to preserve families and households, and prevent anything that could lead to their destruction. What do you say now, after hearing the warning of the Prophet (peace and blessings of Allah be upon him) about those husbands who say to their wives: "If my brother comes and I am not here, show him into the sitting-room" or a woman who says to a male visitor: "Go into the sitting room" - when there is no-one else present in the house?

To those who take the idea of trustworthiness as an excuse, and say things like, "I trust my wife and I trust my brother or my cousin," we say: do not trust too much and do not doubt too much, but know that the hadith "No man sits alone with a (non-mahram) woman , but the Shaytan is the third among them" (reported by al-Tirmidhi, 1171) includes both the most righteous of people as well as the most immoral of people, and that Islam makes no exceptions whatsoever in such reports.

This is the problem. A man marries a woman and brings her to his family's home, where she lives happily with him, then his younger brother starts to enter upon her when her husband is absent, and they begin to talk in an affectionate or even passionate manner. This leads to two things: she begins to detest her husband, and grows attached to his brother, but she cannot divorce her husband, or do what she wants to with the other. This is the grievous torment. This story represents one aspect of corruption, besides which are other kinds which reach the level of immoral sexual conduct and illegitimate children.
Can wife travel with husband’s brother?
In answer to the second question, a woman is not permitted to travel with her husband's brother , who is not her mahram, because the Prophet (peace and blessings of Allah be upon him) said: "A woman should not travel unless she is with a mahram, and no man should enter upon a woman unless she has a mahram with her." (Al-Bukhari, 1729)
Among the conditions of a mahram for travel purposes are: he should be someone whom she is permanently forbidden to marry, such as her grandfather, father, brother, paternal uncle, nephew, etc. 
And Allah knows best.