"I guess theres more to understand but I feel like since he's here now, he should adjust to us"

You are the adult, or at least the older person.  You have more control over your feelings and more choices about what to do than a child does.  It is your place and your responsibility to adjust to a child's needs, not his responsibility to change himself to make you happy.

You have been given a little bit of power over a child and it feels like it has gone to your head.  It is YOUR job to deal with your anger.  It is YOUR job to deal with your jealousy about your sister's boyfriend.  It is YOUR job to provide a good example to a child who will one day hopefully be an intelligent adult -- one who will remember how you treated him.

Now... it is his mother's responsibility to see to your nephew's schooling.  If she has delegated this job to you, it is best to sit down together with her and your nephew and explain the schedule that you will be following.  If he knows what to expect then he will eventually settle down.  He will probably test the limits sometimes, and that is necessary for a child to grow up into an independent adult.  If you try to crush his will then you will end up raising a doormat that will not be able to function well in society.

Also look carefully at yourself and your motives and behaviour.  You are not going to teach your nephew to be a polite and respectful person by being impolite and disrespectful to him.  You may teach him to put on a mask to keep you from hurting and punishing him, but he will never trust you or have a good relationship with you.  Children are not stupid.  You have to act consistently and from good motives, or he will learn that you are a hypocrite who cares more about your own ego than about him and his well-being.

"and for some reason her boyfriend is really good with him and it angers me because I wish it was like that here too."

Trust and respect are earned.  You do not get them automatically.  You have to work for them.

Remember that a leader is also a servant.  Leaders get to lead because they serve the best interests of the people that they are leading.  Leaders are given trust and respect when they have proven their service to the people they are leading.  Leaders who don't understand that they have to benefit their followers quickly turn into tyrants and abusers.  Be very careful that you don't walk that path because you are not ready to deal with helping to raise a child.

Is this the time to talk about how I taught by niece the times table? My sister and her family came to our place and I was playing Zoo Tycoon. She asked if I could help her daughter and I was like yea sure. Now, my method wasn't the best I know that. But it worked. I put her in a chair, locked the door to my room. Put out animals in the times table, and asked her: "How many zebras are there?" (let's go with 6), and then I'd set out for for the times 1, and simply ask how many there where then. And then repeat. I didn't let her out until we'd gone through the 9 xD I'm such a great aunt xD
In all honesty it shouldn't really matter where he's studying, now I don't know the boyfriends methods, but I know my nephew was a little shit to teach, because his grandma (father's side) let him do pretty much whatever, so it was a pain to even babysit him. But I think a reward system would work well with him. Like possibly have a few snacks at the ready, healthy ones possibly like carrots and dip. I know one time when I was babysitting my niece and nephew, they were being such a pain, so I told them if they behaved we'd bake a mudcake after dinner.
Bribing with something nice works most of the time. Atleast it has for me. I mean I got a cookie each day I went to school in the 9th grade xD