Unfortunately I don't think you are going to find any shops renting firearms. There are some things you can do before you start.
A few things that might help you find a gun for her is to confirm her height, weight and her length of pull. Length of pull is probably the most important of these. A relatively accurate method of doing this is to measure the distance from her bent trigger finger to the inside of her elbow joint while holding her arm out to he side and bent at 90 degrees.
Watch a few you tube videos showing the proper method of mounting a shotgun and proper stance. If she doesn't do these properly she will feel recoil much more than if done properly. Just type " mounting a shotgun correctly" on you tube will bring up a number of them.
If you shoot at a club now try to see if one of the better shooters would be willing to help her for a round or two. A lot of ladies will listen to someone new to them far better than their spouses.
Hope this helps. I am in no way trying to belittle your ability as a shooter or a teacher.