S.T.
I think that Karen's idea of the marbles sounds really good. I have heard of doing this with poker chips. I'm thinking they might be better than marbles because if your children are really out of hand, they might throw the marbles!
One suggestion I would have with this idea is to limit the behaviors at first. Don't try to change every bad behavior and reward every good behavior at once. Choose maybe two bad behaviors and start with those. You could even try to talk with the kids to decide which behaviors they want to work on first.
Over the years with both hyperactive children of my own, and a class of "special" seventh and eighth graders I have had a lot of success with the idea of points and prizes. I think simplicity is the key. For instance, with my class, I gave points for very simple behaviors: Be in your seat when the bell rings, feet on the floor, with sharpened unbroken pencil, notebook and leisure reading book. The points accumulated were used in an auction for small prizes and rewards. When "my kids" went on to high school, I was told that they had never seen problem kids come in ready to learn as these kids were! At home, every day after they left for school, my kids got points for dirty clothes in hamper, dresser drawers closed, quilt neat on bed. After they got a certain number of points, they were allowed to purchase a book from the bookstore and had a name plate with their name in it in the book. Consequently, as the mother of seven, I was faced with less mess, and my children all became readers. But I think one of the reasons for success with these plans was simplicity. After a set of habits is well ingrained, you can then add a couple of others.
I'm also thinking back to my daughter who had two young children, was very hyper herself, and had an easily triggered temper. She would call me in the middle of episodes, and I would just get her to sit down, breathe deeply, and count to ten. Sometimes everyone just needed a snack. Getting some calm into the situation was very helpful. I would suggest making a list of your "triggers" and teaching yourself a calming response to them, so they don't escalate. I have an employee who is a problem, and I have learned to reply to each of her complaints and demands with a soothing "Thank you for telling me." I repeat this over and over. Yes, for legitimate complaints I then try to solve the problem, but I find that almost chanting this mantra gets her calmed down, it doesn't trigger an escalation, and it keeps me from getting involved in an argument. You could use something similar with your children's whining and arguments.
S. Toji