Funny dial-up problem - what's causing it and how to correct it?

My sister and her husband recently moved to a rural area where dial-up is their only internet option. After many complaints of not being able to phone them at night, my brother-in-law bought a little device to hook into the phone line. Supposedly it works with call waiting to allow the phone connected to the computer to ring when they have a call.

It works - sort of. It allows calls to get through, but there are also “phantom” rings when the phone rings and there is just a dial tone on the other end. These can number to one an hour to every five minutes and often the connection is dropped. Makes me crazy when I visit.

What is causing these rings? Are there any adjustments that can stop this?. Or is there other software or devices that would work better? Please don’t suggest cell phones - they dislike them and will not carry them in the house.