A hormone produced by the placenta called gonadotropin can sometimes cause vomiting after a baby is born. It can also be amplified due to the body stress that she has been under. The best thing to do is have your mother go to the doctor and get a checkup if it doesnt stop.
You are very brave of looking out for her and seeing if you can get help for something like this, but hopefully things were taken care of, sorry for answering late. Furthermore, hope the new baby is doing well, and congrats on the new member of the family!
