Hi and Welcome:
I'm sorry you are dealing with so much.
I don't think alcoholism/drug addiction have anything to do with cheating. I don't think I've ever been cheated on. I don't have any proof, but I never had that worry in my most recent relationship. I think anything is possible, but I think it comes down to morals and values.
Read the stickies at the top. They help a lot.
Big Hugs to you!