I had to do the following procedure for my 2 years old son's RP which was approved also this month. Actually our PRO was the one who processed everything but I need to submit all of these as required;
1) I registered my son in Medical Commission (medical not required at his age). For your wife, she needs to pass the medical (blood test, x-ray, etc).
2) Submitted passport size ID with blue background
3) Blood Group from authorized laboratories (ours was in Medical Laboratories in Duhail)
4) I don't know where fingerprinting happens. Maybe in Medical Commission too? I forgot as I did mine 6 years ago :-)
All fees was shouldered by the company.