tiggr, I have three women in my life, my wife and two daughters, and we have done extensive backpacking and hiking over the years. You mention the "trail with no cover." Below 10,000 feet, there are lots of trees for ladies and guys to use for discreet cover. Above treeline, even above Trail Crest, there are huge boulders. Planning ahead is important, that is, picking a discreet place before you get to parts of the trail that may be too exposed (for eyes that may see). You, of course, are important in these situations for standing guard.
I think you may find with the hard exercise in climbing Whitney that a lot of the fluids your wife takes in will be perspired away, which will help minimize necessary breaks. When my daughters and I summited Whitney, they never seemed to have the need for a potty break above Trail Camp, but they did take care of business ahead of time.