Which mobile phone has best and loudest sound, speakers?

Where your parents home is physically located relative to the closest cell site is usually more important than the handset.

AFAIK, the Snapfon service uses Puretalk USA, an ATT MVNO carrier. And Snapfon is GSM only if I remember. It's possible that your parents simply don't live in the correct location for good GSM service from ATT. As an aside note too, in some areas ATT has completely removed 850MHz GSM coverage, so that could play a role since the snapfon handsets AFAIK don't include UMTS technology. If 850MHz frequency band for good in building penetration is gone, you do better w/ a handset that uses UMTS. I would be surprised if T-Mobile was any better, as they have generally less coverage nationally outside of large metro areas than ATT does. If you could provide a zip code where the phone/service was going to be used that would be ideal, and perhaps a major cross street/intersection. Worth checking anyway.

In any case, even a phone with big buttons and a loud speakerphone won't necessarily work well w/o proper cellular coverage. That's where I would start. Also, hearing is subjective from person to person/user, so that's why you won't see many reviews as such. db ratings don't mean much in the context of human behavior/perception.