That is a complicated situation I wonder what the mom's relationship is like with the nephew's teacher.

A lot of private schools have a discount or free tuition for the children of employees. My brother-in-law works for a school like this but my nephew is only four and in preschool and my BIL does maintenance on the school on non-school hours so it's a bit of a different situation. However since it's very common for parents to work at a school where their kid goes there should be some sort of policy in place. Are parents allowed to see their kids during the school day? The wife may not be allowed to interact with her son during school hours. 

Another thing to consider is that if he is in four or fifth grade then that is an age where kids want nothing to do with their parents. You're right that is possible that he is instigating and leaving out some part of the story. But now that there is physical evidence of the bullying the school really has a responsibility to do something. I think your brother needs to bring this to the school and say that if nothing is done he will pursue legal action because his son is being injured at school due to unaddressed bullying. That should get the school's attention.

As someone who's younger brother was bullied in middle school to the point of being bloodied several times and having two parents on the school board, I can say that it's complicated. 

My brother was labeled as the "problem kid" because he is high-functioning autistic. My brother never did the instigating though; he was quiet, a little socially awkward, and generally kept to himself. My brother was beat to a bloodied pulp several times, but the school believed my brother had instigated it. The school refused to believe him for months and my parents (who should have had pull given their status on the school board), were dismissed time and time again. One time, my brother knew these kids were coming to beat him up, so he positioned himself under one of the huge ceiling dome mirrors to take the beating. When he went to the office to report it, they again dismissed him, but my brother knew there was video evidence because the dome mirror he stood under was directly in line with a security camera, so the reflection off of the mirror would have been caught on film. The principal pulled up the security camera footage and sure enough, the whole incident was caught on film via the mirror with my brother being the innocent party. The kids were suspended. 

Schools are terrible about protecting the victims of bullying. Frankly, they don't have capacity for it. The one brother was suspended until years end. Have other incidents occurred since with the other brother? If not, I would leave it alone and see how it plays out. If there are more incidents, then action needs to be taken with the school. Pulling nephew out of school seems drastic. 

Your brother should put it out there on the schools website and social media, that seems to be the only thing that gets their attention now a days.  Here locally we had a mother call out a group of kids and their parents who were bullying other kids...they also reported the kids and their parents to the police.  I'm not sure what the follow up was, but it got the school districts attention because they took the time to address it and send home letters to all the parents detailing how they were going to be implementing stricter rules and recourse if a kid was found bullying other students.

My son had this issue in middle school. A teacher witnessed the other kid repeatedly "flipping" my son's jacket hood onto his face after he told him to stop, then progressed to pushing him. The teacher did nothing and this was during class time. Finally after about 15 minutes, my son punched him and he fell. Several kids who were there told me the same story so i know my son wasn't instigating it at all. My son was suspended 3 days, but wasn't in trouble at home. I let my dad take him fishing. This happened in a classroom full of kids and it was the last instance that i know of that he was bullied. 

I know as parents we aren't supposed to advocate for violence, but I don't know of a better way. As prevention, maybe talk to him about avoiding being in situations where he could be alone with the bullies. Bathrooms are often areas where attacks occur, so he needs to be careful there. If your brother does go this route, he should teach him some self-defense skills or get him some lessons, then instruct him that if/when he does fight back, to do it in front of a lot of witnesses, preferably some male teachers who can quickly break the fight up. The kid has already been injured despite his parents going to the school administrators. It's sad that they pay for a private education and still have to deal with this, but it looks like the school isn't going to help. True bullies will prefer easy targets. If the boy is seen as someone who will fight back, they will hopefully see him as not fun to pick on and not worth the trouble. 

I think it might be best for your brother to handle this. Leave his wife out if it as she works there.  And he does need to be the squeaky wheel or nothing will get done.  Exposure to public knowledge is most effective in my experience.  Administration does not want to be found slacking in this day of school shootings.  Use that for leverage.  

Where we live the private schools still have to follow the guidelines that the state has in place for no bullying in schools. If the schools, private or public do not follow the rules, then you can get the police involved. If other people saw you nephew get punched, then tell your brother to go to the police and file assault charges against the bully. If the nephew had to go to the doctor for the bloody nose, send a copy of the receipt for the medical to the bullies parents and the school for them to pay, if they don't take them to small claims court. 

Another route to go with this is file harassment complaint with the police, or at least have the police document, each and every time this happens. Schools are supposed to be a safe place for kids to learn, not a place where they are harassed or beat up.

7 years ago, I went full on scorched earth with a public school, my youngest GS was being harassed, bullied, beat up and the school did nothing. The final straw was when the bully slammed a door on GS11 fingers and broke 3 of his fingers. We had our own documentation from GS friends writing statements, videos from the school bus of the bulling. I went ot the principal and he blew me off, went to the district office, same thing, just poo poo'd me that boys will be boys. Do not ever piss off this grandma. The next step was going to the sheriff's department and filing a complaint for assault, harassment. We went directly to the DA's office and told them that I sincerely hope they follow through on this issue or it would be come a very large matter on every social media and news station that I could get to air the problem and that I would make sure that the DA's office would be the main cause of justice not being served.

I also contacted CPS, to file a case against the school and the bullies parents, for innocent kids being exposed to violence in a supposed safe environment. We have a friend that was an attorney that was giving us all the advise for free and was willing to go to court with us to solve the problem. The bully was charged and got probation, the parents and the school had to pay all medical and therapy bills for GS for that school year.