I've been in (what I thought) was a wonderful relationship especially after being married to an abusive alcoholic. I found a man who was great to me was, and most important, is amazing with my children. After three years of living together, I found out he was having phone sex, watching porn. After I caught him the first time, I've caught him again, two more times. I'm so confused about what to do.

Was it phone sex or was it porn. They are not the same thing.

After an abusive alcoholic I would imagine anyone would seem better, but truth be told, all men (and women) have flaws and unfortunately it does take years of being together to find out the true nature (and flaws) of the partners we pick, and decide if you can work through those shortcomings we discover, or not. If whatever the issue is cannot be resolved to the benefit of you both, through honest communications, then the relationship/marriage seldom works.

When one of you becomes unwilling to KEEP working on the relationship, then you have little choice but end things, and go about your own business. So either you work it out together, or work it out APART. What was the agreement/resolution the first time he got caught? Do you constantly check behind him, and keep catching him?

I also agree, is he texting sexual things to friends or co workers or watching porn on his phone

Watching porn is not cheating, has nothing to do with his feelings about you. Texting sexual things to other women is cheating