Can he accept money in return for being beaten and humiliated in front of people?

Firstly: 

There is nothing wrong with referring for judgement to those traditional councils with which people deal to resolve conflicts and disputes, so long as the one who is passing judgement has knowledge of sharee’ah so that he can judge between people in accordance with that which Allaah revealed, and not according to whims and desires or traditions and customs, many of which go against the rulings of Allaah. If they rule in accordance with the rulings of Allaah, this is what is desirable, but if they rule in ways that go against the rulings of Allaah, there is no point in their rulings, and it is a false ruling and must be rejected. Allaah says (interpretation of the meaning): 

“Do they then seek the judgement of (the days of) Ignorance? And who is better in judgement than Allaah for a people who have firm Faith”

[al-Maa’idah 5:50]

Secondly: 

The scholars differed concerning the ruling on slapping, punching, etc, and whether qisaas or ta’zeer punishment is required in such cases. The majority are of the view that ta’zeer is required but there is no qisaas. The Sahaabah (may Allaah be pleased with them all) and the prominent scholars were of the view that qisaas is required. 

Imam al-Bukhaari (may Allaah have mercy on him) said in Kitaab al-Diyaat, under the chapter heading “If a group of people have killed or injured one man, do all of them have to pay the diyah or be punished with the law of qisaas?” 

Abu Bakr, Ibn al-Zubayr, ‘Ali and Suwayd ibn Muqarrin ruled that qisaas was required in a case of slapping. ‘Umar ruled that qisaas was required in a case of striking with a stick. ‘Ali ruled that qisaas was required in a case of three lashes with a whip. And Shurayh ruled that qisaas was required for a case of lashes and scratches, i.e., wounds. End quote  

This view is the correct one. Those who narrated that there was consensus on the opposite view were wrong, rather if anyone were to claim that there was consensus among the Sahaabah on this ruling, they would not be far off the mark. 

Ibn al-Qayyim (may Allaah have mercy on him) said:  

The people differed concerning this issue – which is qisaas in cases of slapping, beating and other things in which the person who is retaliating cannot do the same to his opponent as was done to him in all aspects – is qisaas justified in this case, or should a punishment of another type be meted out, which is ta’zeer? There are two views: 

The more correct view is that qisaas is prescribed in such cases. This is the view of the Rightly-Guided Caliphs, as was proven from them and narrated from them by Ahmad and Abu Ishaaq al-Jawzjaani in al-Mutarjim. This was stated by Imam Ahmad, and our Shaykh (may Allaah have mercy on him) – i.e., Ibn Taymiyah – said: It is the view of the majority of the salaf. 

The second view is that qisaas is not prescribed in such cases. This is the view narrated from al-Shaafa’i, Maalik and Abu Haneefah, and it is the view of the later followers of Imam Ahmad, to such an extent that some of them narrated that there was consensus on the ruling that there is no qisaas in this case! 

But that is not the case, rather the reports that the consensus of the Sahaabah was that qisaas is prescribed are more likely to be true than the reports which say that there was consensus that it is not prescribed. It is proven from the Rightly-Guided Caliphs and no opposition to that is known. 

Both views are based on the fact that Allaah has enjoined justice in that, so it remains to be seen which of the two options is closest to justice? 

Those who say that qisaas is not required say that retaliating in like manner is not possible in this case, so it is as if justice requires using another form of punishment, which is ta’zeer. Qisaas can only be by retaliating in like manner, hence it is not required in the case of wounding or cutting, unless it is possible to do the same things. When it is not possible to retaliate in kind with regard to wounding or cutting, then we have to resort to the diyah idea, and the same applies to slapping and the like, where we have to resort to ta’zeer if retaliating in like manner is not possible.  

Those who say that qisaas is permissible say: Qisaas in such cases is closer to Qur’aan and Sunnah and qiyaas (analogy) and justice than ta’zeer. As for Qur’aan, Allaah says (interpretation of the meaning):  “The recompense for an evil is an evil like thereof” [al-Shoora 42:40] and “Then whoever transgresses the prohibition against you, you transgress likewise against him” [al-Baqarah 2:194].

It is well-known that responding in kind is required according as much as possible, so a slap is more similar to a slap than ta’zeer, and a blow is more similar to a blow than ta’zeer, because the ta’zeer may be a blow in a different place, that does not resemble the original blow in type or location, or extent. So you are trying to avoid the unavoidable difference between two slaps and you ended up with a greater difference (by choosing ta’zeer) without any evidence from texts or analogy.  

They said: As for the Sunnah [Ibn al-Qayyim (may Allaah have mercy on him) quoted a number of ahaadeeth which prove that qisaas is allowed in such cases]. Then he said: If there was no evidence concerning this matter except the practice of the Rightly-Guided Caliphs, that would be sufficient evidence. 

Haashiyat Ibn al-Qayyim ‘ala Tahdheeb Sunan Abi Dawood (7/336, 337). See also: al-Fataawa al-Kubra (3/402). 

Thirdly: 

Once it is proven that qisaas is prescribed for the beating you received from the other party, you have the option of forgiving him and letting him off if you think that he regrets it and has prayed to Allaah for forgiveness and has apologized and set himself straight. Or you may retaliate (qisaas) by doing the same as was done to you without overstepping the mark or wronging him. Or you may forego your right to qisaas in return for some material compensation as determined by the shar’i judge. 

If you take retaliation by doing to him the same as he did to you, then it is not permissible for you to take any money in return for the humiliation, because you have taken your right. By the same token, any compensation that is awarded to you is in return for the beating, not the humiliation, because humiliation is an intangible harm, and it is not permissible to take material compensation for this kind of harm. The majority of scholars are agreed on this point. 

It says in a report of the Islamic Fiqh Council (no. 109 (3/12): 

The kind of harm for which it is permissible to receive compensation is actual material harm … it does not include intangible harm.  

It says in al-Mawsoo’ah al-Fiqhiyyah (13/40), under the heading “Compensation for intangible harm”: 

We have not found any of the fuqaha’ who discussed this, rather it is a modern idea. We do not find in the books of fiqh any faqeeh who spoke of financial compensation for any kind of intangible harm. End quote. 

In conclusion: What you are entitled to is qisaas, or letting him off completely – which is the best choice if it seems that he has mended his ways or regretted it – or accepting compensation in return for having been beaten. If you avail yourself of the right to qisaas, then you have no right after that to any money. But if you are going to take your rights in the form of money only – which is what seems to be the case from your question – then there is nothing wrong with you making use of it for yourself or giving it in charity. 

And Allaah knows best.