I have the luxury of living miles away from my relative with alcohol problems (younger brother).
But I have thought a lot about it after seeing several posts around here.
I'm fine with my children seeing relatives when they are sober/clean. They can come over to visit, for meals, to play and have family time, etc. If they have alcohol or drugs in their system they can go sleep it off at their own home, go check into rehab, or spend a night with a friend. I will not allow anyone who is abusing substances to be high/under the influence around my kids or in my home. I would not allow anyone with a substance abuse problem to be unsupervised with my child (even when they are clean), and I wouldn't have them living with me.
That's my two cents.