Your wife has my sympathy. Peritonitis can be a very painful and distressing experience and I'm really glad that she is doing well now. There are many possible causes of peritonitis and some of them could be related to her hysterectomy, but it is unlikely that the hysterectomy alone caused it. I will explain.
Peritonitis is caused by inflammation of the outer lining of the intestines. It is usually caused by infection. An intra-abdominal surgery
such as a hysterectomy certainly can cause peritonitis, but is sounds like the surgery and the peritonitis were years apart. This means that the surgery itself could not have been directly responsible. However, surgeries such as a hysterectomy can leave behind scar tissue in the belly which can result in an intestinal obstruction. In extremely severe cases of obstruction, there can be perforation of the intestine which can cause peritonitis. This requires immediate surgery. If your wife did not receive this surgery than it probably wasn't the cause of her peritonitis.
The best type of doctor
to see about this issue is your wife's primary care physician
(if you have one you are comfortable with). It would not be a bad idea to schedule an appointment to discuss the issue so that you can be sure to do everything possible to prevent this from happening again. Good luck.