Is he obliged to attend the waleemah when there is someone there who will offend him with his words and actions?

Firstly: 

If the waleemah is for a wedding, then it is obligatory to attend it, for the one who is invited personally, according to the majority of fuqaha’. 

But if the invitation is general, and he is not invited by name, then he does not have to attend. 

Ibn Qudaamah (may Allaah have mercy on him) said: Ibn ‘Abd al-Barr said: There is no difference of opinion among the scholars concerning the fact that it is obligatory to attend a waleemah for the one who is invited to it, so long as there is no idle entertainment in it. This is the view of Maalik, al-Shaafa’i and Abu Haneefah. 

It was narrated from Ibn ‘Umar (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “If one of you is invited to a waleemah, let him attend.” According to another version: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Accept this invitation when you are invited.” Abu Hurayrah said: “The worst of food is the food of a waleemah to which the rich are invited and the poor are ignored. Whoever does not attend has disobeyed Allaah and His Messenger.” Narrated by al-Bukhaari. 

What is meant – and Allaah knows best – by the words “the worst of food is the food of a waleemah” is the food of a feast to which the rich are invited and the poor are ignored. It dos not mean that the food of any waleemah is the worst of food. 

But it is only obligatory to attend for one who is invited specifically, when a man or a group is invited by name. But if someone issues an invitation and says, “O people, come to the waleemah,” it is not obligatory to respond, and it is not mustahabb to do so. Rather it is permissible to accept because one is included in the general invitation. End quote from al-Mughni (7/213). 

Secondly: 

If there are people at the waleemah who will cause offence, it is not obligatory to attend. This is an excuse not to attend. 

This was stated by some of the fuqaha’. In that case he has to apologize to the one who gave the invitation, or attend for a short while and leave quickly. 

It says in Tuhfat al-Muhtaaj (7/430), where the conditions of it being obligatory to accept an invitation are mentioned: There should not be in the place where he is to attend anyone who will offend the invited one by means of outward hostility or destructive envy (hasad), or anyone with whom it is not appropriate to sit, such as vile and despicable people. End quote. 

Thirdly: 

If the waleemah is not for a wedding, it is not obligatory to attend, even if one is especially invited to it. 

Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (7/218): The ruling on accepting invitations to circumcision waleemahs and all other invitations except to weddings, is that it is mustahabb, because it involves offering food to people. But accepting the invitation is mustahabb, not waajib (obligatory). This is the view of Maalik, al-Shaafa’i, and Abu Haneefah and his companions. End quote. 

Based on this, there is no sin on you if you do not attend these waleemahs, if they are not for weddings. 

Fourthly: 

For a woman to uphold ties of kinship with her brothers and sisters is something that is confirmed in sharee’ah, because of the commands to uphold the ties of kinship that are mentioned in the Qur’aan and Sunnah, and the prohibition on severing those ties. This upholding of family ties may be achieved through visits, phone calls and asking after family members, depending on what one is able to do. 

You should not fall short in this great act of worship, and not let your brothers’ coldness and lack of kindness push you to do that. You will be rewarded for upholding ties with them, even if they fall short towards you, because the Prophet (peace and blessings of Allaah be upon him) said: “The one who upholds the ties of kinship is not the one who reciprocates, rather the one who upholds the ties of kinship is the one who upholds those ties even if his relatives cut him off.” Narrated by al-Bukhaari (5645). 

The one who reciprocates his relatives, and returns favours and treats them well if they treat him well, is not the one who is upholding ties of kinship as required by sharee’ah. Rather the upholding of kinship ties that is required in sharee’ah is that which involves treating relatives well even when they treat you badly.  

But if meeting often will cause annoyance, there is no sin in reducing the frequency, whilst remaining in touch at infrequent intervals or by phone, etc. 

But it is better to hasten to remove the misunderstanding between you and your brothers, and try hard to improve your relationship with them. That is better for all of you in this world and in the Hereafter. 

And Allaah knows best.