Emotional abuse - how can I prove it?

My husband withholds love from me and he excessively views pornography. He is mean to me and the kids but has never hit me. I have now 'caught' him on Web sites for meeting other women who want to have sex..some sort of 'hook up' Web sites. All of this and more has caused me great emotional distress. Is there such a thing as 'emotional' and 'mental' abuse? Or is abuse only physical? I don't want to cause the kids the pain of divorce & because I feel I would have to leave them alone with him if divorced I stay with him. It seems like wether I stay or leave I loose. He drinks & drives and over drinks so I am afraid to leave the kids alone with him for their own safety. But how do I prove any if this? He says to me... "prove it" "good luck proving that" and so I feel trapped in this very unhealthy marriage. The thing that made me feel the worst was when he told me "you are completely useless" infront of the kids. I'm more afraid to leave then I am to stay mostly because I don't trust him alone with the kids..due to the things mentioned above. If he is abusing me is he right..would I have to prove it to make sure the kids wouldn't be alone with him if divorced?