Hi april rain,
re your comment:-
"And while his problems are bad, are they bad enough to break up our little family over?"
In a word, yes. Sorry to be so blunt here but being a child in a household where a parent is an alcoholic is a bloody nightmare for said child with far reaching effects that often extend into their own adulthood.
Your cons list therefore mightily outweighs any pro list you draw up. The first two cons alone would be dealbreakers.
What do you get out of this relationship now?. How can a man who is short tempered with the DC be at all seen as kind (to you anyway?).
Alcoholism is never a good thing to be around; your children will become caught up in that as they become older. You as his wife are already enmeshed within his world of alcoholism and have doubtless made many excuses for him and to your own self. You are his enabler and you are playing that role within this dysfunction.
How many people in your real life circle know about his alcoholism; very few I would daresay. Alcoholism too thrives on secrecy.
He may well love you (how does he show this?) but he loves alcohol more. Alcohol is a cruel mistress and his primary relationship is with drink.
He will not stop drinking either because you tell/ask/plead with him to stop drinking.
The 3cs re alcoholism are ones you would do well to remember:-
You did not cause this
You cannot control this
You cannot cure this
You may well be doing yourself a favour by speaking to Al-anon and working out whether you want to hang around for the next 5-10 years or so. But I will tell you this, your children won't ultimately thank you for staying with their drunkard father if you did so and could well wonder why you put him before them.