Hi Riley,
As you now know it is the painting of the stained cedar without the proper primer that is haunting your family. It is that underlying layer of paint that is causing the continuing problem. The paint coat did not bond well with the stained cedar surface, therefore additional coats of paint does not get at the problem and could make it worse. However, you do have a few options.
The best, and most likely the most expensive, is to remove all of the previous coatings. I would suggest using a stripping system such as Peel-Away. Peel-Away is applied like paint, plastic sheeting is then applied to the surface and allowed to set for a few days. When the plastic is removed so are all the previous coatings. The surface is then neutralized and pressure washed. If you want the look of paint you can then apply a high quality Acrylic Solid Stain. (End of peeling problem )
The next best option ( be aware that this may not stop the peeling problem ) is to do as your painter has suggested, that is to remove peeling areas and try to stabilize the coatings with a primer. Your painter might consider using a binding agent such as Peel-Stop instead of a standard primer in areas where all of the paint is not removed. Apply a high quality Acrylic Paint ( Solid Stain is not an option unless all of the old paint is removed.)
Peel-Away and Peel-Stop are available at Glidden and Dulux paint stores, however most paint companies offer similar products.
Hope this Helps
rmichael / pro painter