How can one deal with the fear of children becoming so attached to their grandmother that it feels as though she will replace their mother, and the consequent decrease in visits and marital problems?

This fear is a whisper from Satan, to make disobedience and cutting ties of kinship seem appealing. Your children's grandmother is their second mother, and cutting ties with her is one of the greatest major sins. Allah Almighty says: "So would you, perhaps, if you turned away, cause corruption in the land and sever your ties of kinship? Those are the ones whom Allah has cursed, so He made them deaf and blinded their vision." Cutting ties with her causes problems with the wife and relatives. The cure for delusions is by fearing Allah and obeying His command. The grandmother cannot replace the father; this is from the whispers of Satan.