L.S.
Try the "To Train Up a Child" discipline book by Mike and Debi Pearle. They also have a series called "No Greater Joy" available. www.nogreaterjoy.com
The problem is not necessarily a time problem as much as a selfish, discipline and respect problem. And it is your job to train them in those things also, in addition to giving them time and understanding. I would think that with that many you would have some sort of schedule. Like kid #1 mom Monday dad Tuesday, Kid #2 mom tuesday dad Wednesday, Kid #3 mom wednesday dad thursday. etc.
you can also www.duggerfamily.com about the mom that is pregnant with her 18th baby, yes 18th and see how she handles the alone time issue. i think she schedules it, but i know the issue is on the website.
i only have 3 boys and have those problems, but find that they are less with more discipline and activities. the boys are bickering and fighting when they have to much unstructured time without an adult and then we see the same things. discipline works wonders. chores do to. and acitivities make them to tired to bicker. bike riding, gymnastics lessons, swim team. walking, mowing the yard, running with the dog, skate boarding etc.
good luck,
L.