Kids understand more than we think. Not sure you can just dismiss this as her being jealous of your new relationship.
I disliked my stepmom. Not because I was jealous of their relationship, which she and my alcoholic father both decided was the cause, but because I saw how much being with her changed his personality. He was enthralled with her and their relationship was a very typical enmeshed alcoholic/codependent dance (she had alcohol and food issues and they were very codependent on one another). He began treating my brother and me as second class citizens in order to prove his love and loyalty to her because we were reminders that he'd been married before (she had too, three times, but that never got brought up, oddly enough). Her daughter lived with them full time and was treated like an only child. My dad was over the top nice to her while verbally and physically abusing his own children.
Not saying that you are going to that extreme, but it sounds like this relationship is causing you to change you standards.
If I may ask, why are you so sure that this barely-recovering, dry-drunk alcoholic is ideal relationship material for you? Because he is nice to you and likes to do things outside? I think you can find a sober man who meets those criteria. What is it that is truly attracting you to this man?
He wants to go slow, if it were up to you what would the pace be? Sounds like you are eager to jump into this fiasco with both feet. Why?
Sorry if this is harsh, but I did the same thing in my last relationship, which was with an alcoholic. He ended up treating my oldest son like dirt after being really nice to him in the beginning. I ignored the red flags and dove right into it, so I am speaking from my own bitter experience.