When one of the parents is also a stutterer he or she will be even more likely to feel that guilt and I wish to say that it is usually unmerited. Stuttering is not caused by imitation. If you will observe closely you'll find that your child's stuttering does not resemble yours.
Although some strains of stuttering tend to run in certain families what is inherited is not the stuttering but a neurological predisposition to it so there's no need to blame yourself for that. Your child needs you love, not your guilt so relax, my friends.
Most children who begin to stutter get over it by the age of six. Learn what you can do to help them do so. For those who don't, seek the aid of a speech therapist who will show your child how to cope with it.
All three of my own children went through a period of stuttering but now as adults are completely fluent. One is even an ordained minister. Only one of my nine grandchildren stuttered for a short time and my great grandchildren do not stutter. I believe that ours was a very happy home and since both my wife and I were skilled therapists with stutterers no stuttering in our children should have occurred but it did and I don't think it was our fault in any way. If you have sinned, your sins were small, small sins and you need no penance. So stop blaming yourselves.