1. Percy met Audrey when she came to work in the Muggle Liaison Office at the Ministry. Audrey had issues with her family, too, since she's a witch, and they are Muggles, and was very understanding of Percy's estrangement from his family. Percy realized how long it had been since someone had listened to him.
2. Audrey encouraged Percy to reconcile with his family. He started the process by saying hello to his father in the corridor at the Ministry. Audrey said she was proud of him.
3. Being Muggleborn, Audrey was Undesirable #17, and did not appear for her hearing. She had to go into hiding. Percy was distraught when he couldn't find her, and fretted until receiving a surprising owl from an unexpected person--Neville Longbottom, who invited Percy over and told him, in person since owls can be intercepted, where Audrey was. Augusta Longbottom went to Hogwarts with Audrey's great aunt, her only magical relative with whom Audrey went to stay.
4. With Audrey's departure and observing the ministry hearings, Percy realized with certainty that he had been wrong. However, he had to stay alive and out of Azkaban long enough to admit it to his family.
5. Also due to Audrey's influence, Percy realized Fred and George's products were brilliant, and became a regular customer. He even has a pet pygmy puff.
6. Percy's daughters are Beaters for the Gryffindor Quidditch team. His niece Roxie is a Prefect who dislikes Quidditch. He and George often joke that their daughters were switched at birth.
7. The main thing Percy learned from the war was that work is NOT more important than family. He was very thankful he had the chance to reconcile with Fred before his death, and with the rest of his family at various times. But the first time he held Molly, he no longer cared about being Minister of Magic, he only wanted to be a good dad.
It occurred to me while writing this that most of these are explained in my Percy/Audrey epic "A Year of Worry and Hope." Oh well, at least the universe in my head is consistent. ;)