"Discipline" in its purest form means teaching. When the example set by nurturing adults is strong, positive, and respectful, kids will turn out strong, positive, and respectful. They learn far more through imitation than through any amount of verbal instruction or punishment.
It sounds like you're already doing a lot of things right. A bit of expert coaching might help you reach the next level of excellence.
I strongly suggest you get yourself a copy of the fabulous little book How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish. It won't conflict with anything the parents do, and the wisdom in this book will make it a resource you reach for again and again. We use these techniques with my 4.5yo grandson, because they work brillliantly.
One example: Physical rewards and charts for good behavior are not nearly as effective as when adults remark with calm admiration when they see the child do something positive. Examples are, "I noticed how carefully you put that together." or, "That was hard to do, but you kept trying until you did it!" or, "It felt so good when you told me thank you." or, "Hmm, how did you figure that out?" or, "I see a boy who picked up his game without being asked." or, "You chose your outfit today? I like those colors together." or, "I'll bet you can figure out a good way to do this – will you please help me?"
Think about how great you feel when people notice your efforts. Kids love that, too, and are motivated to get more of it. This is only one of several tips and techniques available in this wonderful book. There are ways to get the child involved in solving his own problems, ways to present your needs to him so that he can recognize and respond positively, ways to find "natural" consequences for mistakes, and more.
Using this book has eliminated the need for virtually all punishment or "correction" from my grandson's life. He'll occasionally take himself into a sort of time out when he needs to get his emotions under control, but that is his choice. He's polite and cheerful, and super-motivated to be part of a family team, because he understands the family is on his side. I think you'll agree that How To Talk/Listen could be the best investment you've ever made when it comes to working with kids.