Firstly, I'm so sorry you're this unhappy, but let me honestly tell you that staying with the partner for the sake of the kids won't work. Its a wonderful thing to think about your kids, but all kids want at the end of the day is their parents happy, and you are most obviously not. I watched my mum and dad try to stay together and knew even at the tender age of twelve that they were not happy. I saw other kids parents cuddle, kiss, make romantic gestures to one another, while mine just seemed unhappy, angry, and lonely, despite us all living in the same house. It was awful, in the end it was me who begged my mum to divorce my dad! (Now they are good friends)
You deserve to be with someone who worships the ground you walk on! I too have had a relationship break down with children involved, and knew I could never be the best mum I could be staying with their dad, he too drank and even one time hit me in front of our baby son, and I decided there and then, I didn't want my boy to grow up thinking that was normal, so I have been a single parent, and stayed that way for seven years, I got strong and finally realised I didn't need a bloke to make me strong, I had me! :-)
Your kids will be upset and angry if you do divorce their dad, however, this will be short lived, just be honest with them, don't down their father, just tell them that you need to do this to be happy, and they will understand.
No-one deserves to be with someone who treats the like rubbish, just imagine what you would say to your own child if they came to you asking for advice on this very same thing. Would you want your child to be in a relationship like yours? Being shouted at, cheated on, made a fool of? Of course not, and you are worth just as much as your children, and you deserve to be treated like a queen. I hope you find the strength in you to make yourself happy, because your kids follow your example, and if you show them strength and how you won't be treated like a doormat by anyone, then they won't grow up to be treated like that either.
Loadsa love & strength chick xxx