Norah - I'm another one who feels strongly about this issue. Your comment that "it is the parents who have rights over their children" is imo, both legally and ethically incorrect.
Parents have responsibilities to their children. Those responsibilities include meeting their emotional and developmental needs and keeping them safe. It goes without question that parents who experienced abuse either directly from their parent or because of neglect/ lack of protection, will be wary of history repeating. Those are the parents who are likely to have our understanding when they refuse to allow their children to spend time with grandparents.
The children are, quite rightly, the individuals who have "rights" here.
I agree with the points Smileless makes, although in some circumstances, it would be difficult to arrange contact between adult children and their parents. Animosity and anger can spill over into contact sessions. The kind of parents who try to turn their children against the other parents are likely to repeat that kind of emotionally damaging behaviour in relation to the parents they are estranged from.
I feel for Smileless, making the decision not to try and insist on a relationship with her grandchildren in the face of the breakdown in the relationship between she and her husband, their son and daughter in law. It's rarely the case that people have somehow "deserved" to be cut off from grandchildren, alongside losing their own adult child. Heartbreaking isn't an exaggeration. Some compassion for everyone in this rotten situation wouldn't go amiss.