I am looking to purchase a secondary camera that meets the following criteria: 1) Compact enough to be inconspicuous for street photography. 2) Simple enough that I can hand it to a friend/family member (of a variety of ages) and they can participate on a shoot with little explanation from me and/or frustration from them. 3) Inexpensive without sacrificing image quality.
1) For inconspicuousness in street photography, waist level shooting seems to be an effective technique; so you'll need an articulating screen to be able to compose before shooting from hip.
2) The whole idea of "point and shoot" is that you can point it at something and click button to shoot an image, so I don't think simplicity will be a problem unless you insist on your assistants to change some settings or shoot with manual exposure/focus - in this case, complexity comes from you, not the camera.
3) Cheap, good, fast - you have to pick two in this world. Since you have picked cheap and good, looks like you have to give in in terms of time. Either look for a used upper level model from past, or wait until current top-level models become available second-hand. For maximum image quality, you want a point-and-shoot that performs well in low light, because that's where the differences are most discernible. Cameras with big sensors (measured by physical dimensions, not in megapixels) have a clear advantage, but AFAIK those are all quite recent models.