Rufus should have been like every other pureblood. In fact, he had been destined from birth to be like every other pureblood, as, for quite a long time, his mother was engaged to a Parkinson man. Unfortunately, life for Rufus and his mother didn' unravel according to plan. Griselda had it all figured out until she fell in love with the adopted Parkinson.
The Parkinson's as a pureblood family would never adopt someone who wasn't pureblood; Amadeo, while a pureblood, was a foreigner, so even then the Parkinson's shouldn't have accepted him. They were even reluctant to call him "pureblood" given how his ancestors came directly from a mix of Aztec and Spanish wizards. They ended up having to, however, as it was the dying wish of Amadeo's father, their closest global ally. He was despised but tolerated. His charisma and the fact that he was actually Griselda's age is what drew her in.
Griselda's fiance was about ten years older than her. The plan was to marry her as soon as she graduated, but everything changed when she ran away with Amadeo. This cast a stain on the family tree. For a good deal of time, she was outcasted from the Yaxley's. Griselda finally came back, alone, and with a son; Rufus. Her body was covered in bruises. In order to be accepted into the family, she had to state that she had been married and widowed and that she had been forced to marry the treacherous Amadeo. Ironically, although she loved Amadeo, he had been aggressive, ad the truth didn't fall far from the fiction.
No one ever heard from Amadeo, although the Yaxley's carried a personal vendetta against him. Rufus, previously Rufus Parkinson, had his name changed back to Yaxley after such a disgrace to the Yaxley name.
Rufus did his best to live a privileged life, but it was hard when rumors spread that he wasn't pureblood, or when people would laugh at his tan skin. This was due o his hyperactivity- and his love of the outdoors. The best thing Rufus ever did to prove he was a wizard through and through, was to start playing Quidditch. He had a toy broom when he was little, and sometimes he would be put in quidditch little league games against his pureblood friends, but he didn't really enjoy it till his first sign of magic at 5. He had been playing in the Beater position when suddenly the snitch appeared. His little broom wasn't fast enough to catch up to the other five-year-old until by magic, he did, and he beat that little five-year-old to the ground with his fists. Naturally, he stopped being friends with that person, but the aggression of the sport energized him.
Griselda took advantage of his love for Quidditch and put him in intensive training from an early age. If anything, this would be how she would untarnish their name. She made sure to impress upon him, every move he made reflected upon her. Rufus, who loved his mother too much too see she was using him, took this pseudo encouragement and pushed himself to be the best at every position.
Rufus got his Hogwarts letter of acceptance when he was 11, and from there, he studied hard and earned top grades to prove himself to his family. As he grew older it, became more clear to him that, the sport he had put so many tears into, would not be a future viable career path. While it helped build reputation and connections, in order to really untarnish the name, he needed to become something greater. So he did his best in other things, at his mother's insistence, but still dreamed that he could go pro after school. By the time he was in fifth year, he had even been approached with many pro contracts, specifically as a beater (which was his best position), but had to turn them down because of his education. Rufus figures that, someday he'll be able to prove that he can play Quidditch and do some sort of important work in the ministry.
He will now enter his sixth year at Hogwarts.