Would you allow a 4 year and 6 year old to visit their father in prison?
In the end it is up to the mother, but here's how I see things; a drug addiction should not be a crime to begin with (countries that don't criminalize it and work to get addicts help instead of arresting them have lower rates of addiction and the like, for example!) and if he has been clean and serving his sentence then he is proving he is capable of recovery and moving on. A non-violent offense not involving children, which explains why he's in a minimum security facility, should not prevent him from seeing his children.
On top of that the children are asking about him, and if they've asked if he's dead that means they haven't been told where he really is. The mother should start with telling the kids the truth in terms they can understand and see how they will react. Perhaps they will be embarrassed, but they may also be angry at the mother for withholding the truth from them and leading them to ask if he's dead. They may be angry with him, they may not understand, but regardless they deserve to at least know the truth. If they're old enough to ask they are old enough to know even if you have to explain it in a much simpler way, some of the best parenting advice I was ever given from great parents.
If their reaction is a relatively positive one they should be allowed to go see him. The father has the right, and it may even help along the way with his recovery. Drug addicts often go through steps and one of those is to make amends to those you hurt while addicted, he may be wishing now more than ever to make amends to the mother and children for his drug addiction and how it has landed him in prison so he cannot be there for him.