The Lupin, Potter, and Weasley children get no special privileges in their classes at Hogwarts. Any student in the whole building could tell you so.
Professor Potter praises all his students equally and teaches them all the same. You’d never find him over congratulating a Weasley for very minor progress or lavishing undeserved praise on a child of his own. That simply wouldn’t be conducive to a productive class for all of his students. He’d never gloss over the introduction to werewolves just because it might upset Teddy Lupin, no matter how badly he’d like to skip it himself.
The same goes for Professor Longbottom. He may be very good friends with Harry Potter and the whole Weasely clan, but never would he dream of teaching their children any differently than he does every other student. He takes no extra time discussing Mandrakes, even though he knows that James Sirius is fascinated by them. He would never give out undeserved house points. And he certainly wouldn’t give extra detention to their bullies, no matter how much he wanted to.
Professors Hagrid and Weasley, when teaching care of Magical Creatures, would never spend more time on one animal over another because they know a niece or nephew favors them. They stay as impartial as they can and teach all of their students the same. If any one student finds a particular animal intriguing they will simply be referred to a particular book in the library for further reading and told to bring any questions to Professor Weasley in his office.
Headmistress McGonagall, standing at the front of her Transfiguration classes, teaching how to transform a porcupine into a pincushion, looks at each of her students with the same sharp eyes to ensure they are paying attention. Walking amongst them as they try the spell for themselves, she looks on with no particular fondness as Rose Weasely does it in just three tries. The Headmistress swallows a comment on how much Rose is like her mother and gives her the same congratulations she would any other student.
However…
When Harry’s office door opens to reveal a teary-eyed Victoire Weasley, Professor Potter disappears in an instant, replaced by Uncle Harry. And if his own child should say exasperatedly, ‘Can’t you just be my dad for a minute’ he does a dramatic spin and Dad appears on the same spot where professor Potter stood a moment before.
When the greenhouse doors open and Neville comes around the table full of tall tentacula plants to see Hugo Weasley looking overjoyed at his latest accomplishment, Uncle Neville appears from the shell of professor Longbottom. Or when a soft voice calls through his door, “Hey Uncle Nev? It’s Fred, can we talk?” Professor Longbottom disappears in the time it takes to open the door.
When Hagrid hears a knock on his cabin door and opens it to a little troop of Potters and Weasleys he just laughs and calls them all in to have tea and Rock cakes. Or when little Minerva Ruby Potter comes along all on her own, he knows she needs an understanding ear and a few cuddles with Fang 3.
When Charlie Weasley hears a knock on his office door, he puts on his professorial persona, but the minute he catches a glimpse of hair as red as his own he softens up and grins. If Lily Potter should arrive at his door and carefully open it when he says to come in, he’ll never not grin and call her Lil’ Potter to make her laugh.
Minerva knows who’s at her door before they knock, but the Potter, Weasley, and Lupin kids have to say the magic words, “Can you be Aunt Minnie now?” before she’s magically transfigured from stern old Headmistress McGonagall into their beloved Auntie Min.
The Lupin, Potter, and Weasley Kids get no special treatment in class, but they know that if they should ever need their Aunt Minnie or Uncle Charlie or Uncle Hagrid or Uncle Nev, or Uncle Harry/dad, they only need to knock and then close the office door behind them.