So your DD regularly emails you about how naughty one of the children has been.
I am going to offer two or three suggestions which you are perfectly at will to ignore.
1. Are you sure that you are right and she is wrong? I very much expect that you are right, but I do know for instance that my own mum has a slight favorite of one of my children, who happened to be the naughtiest, and she couldnt see it for several years. We never fell out about it, but when said son grew up more, he was quite open about being a bit of a pain and said so in front of my mother, so she then had to concede that she had got things a bit wrong.
2.As kl asks, was there a difficult birth/pregnancy?
3.Does the gc play up often at home, so when mum goes out with him, she is quite strict with him. I have seen this happen with one family, and thought mum, and dad too for that matter were being over harsh. They probably were, but I did not see how the child was behaving at home on a day to day basis, so I only saw part of the picture.
I think that what stands out a lot in what you have written, is how your DD is treating her husband.
Is she under a lot of stress?
Is he not allowed opinions on anything at all that differs from hers?