I have hesitated to give advice here. I have the same unanswered questions as Shannon above. I am afraid that if I took everything away from my kids, they would only get into mischief. I have been looking towards a gentler approach and I highly recommend books by Sally Clarkson to give you an idea of what that looks like, or her blog at http://www.itakejoy.com. You are their mother and you know them best. You need to get to the heart of the matters with each child. Your focus should be more on habits and character now than academics, while still meeting requirements. Do you have a good family read aloud going now for literature? This could be a special time for you all to bond together. Charlotte Mason says that education is an atmosphere, a discipline, a life. Do you have the right kinds of books and things available? You said you do not do video games, but do they have other screen times (tv, computer, iPod, tablet, etc.)? These may need to be restricted, while leaving educational games and living books and art supplies and beautiful music around aplenty. I am praying for you to figure this out soon.
You need a routine or schedule and general rules laid out for your family. And it won’t look like anyone else’s. In Laying Down the Rails, there is a small section on the habit of regularity. It starts with consistent bed times and then meal times and then work in other regular activities. For more on this, I recommend Managers of Their Homes. This will take a while to figure out and implement. Pray about what is right for your family.
A 15 yo can do much on his own. See http://www.urthemom.com and her book. In CM, the 6 yo does not need much academics. She learns through play and she needs to learn good habits now. How old is the son who power struggles over chores? I am hoping some wiser, more experienced moms will chime in here soon.