Al, are you referring to the Apple Watch? Just wondering if your 2nd post was the answer to the problem, or if you still needed help? Apple's design is to have the notifications go to the watch, or the phone, but not both. This is Apple's configuration.
I too have an apple watch and the notification is off but there are time usually first thing in the morning when I don't hear any call from my iPhone or iPad but yet I see messages being left. My volume is up etc but nothing. I have done resets and then it seems to work again. The problem is, I just don't understand why it does this. I will experiment more.