How do you know if your abusive husband is cheating?

I guess I did this wrong... I have been dating someone for 2 years. He lost his wife about 3 years ago, they have 2 younger children. I have never been in a relationship where someone has spoken to me the way he does. He is constantly putting blame on me for his out bursts. His own children think he is psychotic and agree that he snaps out of no where and is just down right nasty. His issues have nothing at all to do with losing his wife. How do you stop the verbal abuse? I love this man, want a future with him but NOT under the circumstances. He is on his best behavior a wonderful, generous man. Will this ever stop? How do you get them to see that they have anger issues and are being verbally abusive, when I draw it to his attention and ask if he would like some man to speak to his 15 year old daughter the way he speaks to me...he says NO, and that I dont deserve to be spoken to that way. My family loves him, so do my children but I am certain that this is not "normal"