Regarding the picture. I don't think it's his wife and kid. In the last episode in his nightmare it looked like a mans hand as it was rather big. I think an accident happened where Du-sik feels responsible and the picture of the women is the wife of whoever died in the accident. Could be wrong, but I highly doubt it's of his wife and kid.
There's proof of SYJ texting him to not touch or kiss the FL and remove scenes from the script while there none…
A statement from her agency is not proof. It's their job to protect the artist so they will say whatever they can to disarm the situation, doesn't make it true. They should release the full texts oh KJH initiating then, if they exist that is, then that would be proof. Yet they didn't and until they do their statement doesn't hold much ground.