Brief Answer:
Umbilical hernia
Detailed Answer:
Hi there..
Thanks for writing in....
Diastasis recti is a gap between the abdominal muscles. You can feel the gap with your fingers. Diastasis recti generally would not cause pain , discomfort or 
nausea.
Ask your father to lie on his back with  knees bent and feet flat on the floor. Place your fingers  just above his belly button. Ask him to lift his head, neck and shoulders slightly off the floor  and you slightly press down with your fingertips. If you feel a gap, that’s the diastasis. You will feel the muscles close in around your fingers as he lifts his head and neck.
The fact that it disappears completely while lying on his back points to a hernia. If the swelling appears or increases in size on coughing or straining, on standing up, more in favour of a hernia.
However, hernia can sometimes cause intestinal strangulation which can cause serious problems and complications like 
intestinal obstruction and 
gangrene.
Other danger signs to watch out for are discoloration of the swelling, 
constipation, 
vomiting, pain etc.
The fact that he has pain and nausea, I would definitely advise that  it would best to consult a surgeon, who might do a physical examination and an 
ultrasound ... and decide on the further management. 
Hope this information was helpful to you.
Regards,
Dr. Divya Kuttikrishnan