Kids need stability more than they need their parents to be happy. They need you to BE THERE ALL THE TIME in order for them to be happy.
Sorry to disagree with you on this, but there are plenty of experts who will also totally disagree with this line of thinking. Staying together for the sake of the kids can cause more harm than good - the kids need stability and they need security, neither of which will be found in an unhappy/unhealthy marriage. What are you teaching them in this instance? That this kind of behavior is acceptable? I speak from experience - having left a 26-year marriage that I stayed in for the sake of my sons, and in the end they suffered a LOT more damage that they are as adults now coming to grips with, some of which could have been avoided had I not remained in the abusive/controlling, and totally UNHEALTHY relationship for THEIR sake. Hindsight is 20/20 and at the time I did what I thought was best, now I am also trying to not beat myself up with guilt for making a poor choice in staying....
“Life isn't about waiting for the storm to pass... It's about getting out there and dancing in the rain."