UPDATE TO LINKED CALLS - SOLUTION FOUND.
I was looking in Settings on my iPhone, for a different reason. Under Settings > Phone, there is a section called "Calls on Other Devices When Nearby." I clicked on this and found Allow Calls on Other Devices. This has a master on-off switch to turn off any other devices. But, when it is on, ALL of my computers, including my practice computers, iPads and iPhones show up as choices. They each have the individual on-off switches next to them. These were all turned On. I didn't do it, directly, but perhaps when I first set up my phone or iPad, it happened. I have an iPhone 6 Plus, now and it was still happening. Anyway, I've turned all of these off and my wife and I are no longer getting each other's calls at the same time. I hope this info will help others in the Forum and it certainly provides a clear answer to the problem. To recap the initial issue, when my wife and I were in my practice or at home, and a person called her iPhone, my iPhone also rang, and vice versa. It made it difficult to know who the caller was trying to reach. For example, our college student son might be needing to talk to my wife about something, and I might answer, or the other way around. Or, a referring doctor calls me and my wife answers. Since we are together, when it happens, we are able to get the correct person on the phone. But, it was confusing for us and the caller. Thanks for all the help in this and other matters.