Thank you for all the feedback! You have all given me some new ideas and encouragement.
I have had many conversations with them about the atmosphere in our home, choosing to treat each other with kindness etc. They do lose privileges for bad behavior, but usually only for the remainder of the day. Maybe I'll try taking away the privileges until they earn them back with good behavior. I know routine has a lot to do with it. We were about three weeks into our summer break when I noticed a significant increase in bickering. We've been back in our school routine for two weeks now and I'm hoping that will help some. Also, I need to be more consistent with consequences. I always intervene and have them apologize (honestly that's gotten lame- it seems so insincere), but sometimes I leave it at that, sometimes they spend sometime in their rooms, lose privileges, etc. I need to decide how I want to handle it and then do it, consistently. Thanks again for the help!