I also think when bickering or mean behavior gets out of hand, it can be because there's not a clear manifesto, if you will, of who your family is and what you stand for. Can you get your kids to buy into/contribute to the idea that you're a family where you do.. (positive attributes) and where you support each other in attaining those goals?
This is a good idea.
I get a lot of mileage out of being shocked. I guess if it happens frequently, you can't really be shocked, but I have said things like, "Wow… I'm so surprised to see this because you're such a kind person. What makes you think that's OK?" I want my kids to think I know they're kind at their core and that bad behavior is not who they are-- seems like if I do that, they don't want to disappoint me.
This is too shame-based for me. DD has a lot of shame already, which is partly her and partly a reaction to not-ideal parenting. Also, it's not shocking anymore, sadly.
I do tell them they are kind people, etc.
I will say that the kids still do have fun together and enjoy each other rather often. I have seen families where there is none of this because the children inhabit very separate spheres, which ours do not. However, I am concerned, because the age difference is going to matter more very soon. DD is growing up. In fact, this could be a hidden but important factor.
