An update on my Kindle Fire, in case this helps someone else. The problem was not the provider. I spoke with the Help folks at Kindle and they got my device back on track. It is possible that, because of the changes the TQS website has gone through, some of our Kindles may not recognize the videos because the internet industry is going through changes too. I don't even understand what that all means, however, the Kindle folks had me do two things and I am back to seeing both the TQS shows AND the DVDs.
The first thing I did was to go into ALL APPLICATIONS and cleared out my data. Yes, you lose bookmarks and other stuff, but it was not a problem for me. When I went back into The Quilt Show, I was able to watch my shows. This helps in case you download apps that react negatively with whatever else is on your Kindle at the time. For example, I had tried to download an updated Adobe Flash Player which is probably what made my system get mucked up.
I still could not get into the DVDs, like the two Miller DVDs that are available for watching right now. To solve this problem, while logged into The Quilt Show, at the bottom of the screen, where there is an icon with several horizontal lines, I tapped on that, found the browser and changed it from "automatic" to "mobile." Now I am able to watch the Quilt Show DVDs and am also able to select exactly what Chapter I want to watch.
The Kindle folks were extraordinarily helpful and did not stop until we had the problem solved. Very happy with their support so that I could get back to watching Quilt Show episodes on my Kindle.
As I said, I don't even pretend to understand what all this means, but I hope the computer experts like John and Bob will be able to interpret all this and make sense of it. I also hope it helps anyone else who is having difficulty with their Kindle. I am now back to watching my shows on the Kindle. Thanks to all who tried to help!