Awesome, thanks so much for the Playground link! If you change the isVertical property there and then look in the console window, you can see that the StackPanel gives a bunch of warnings about using percentage width in a horizontal StackPanel. RadioGroup, it seems, is a convenience class designed to make it extremely easy to create radio buttons formatted in a very specific way.
Fortunately, it’s almost as easy to create radio buttons formatted a different way, we just have to use different tools. I went back to the docs for radio buttons and adapted code from the example provided there, which shows how to create radio buttons easily using a StackPanel directly, thereby avoiding problems where the RadioGroup sets state that conflicts with a horizontal StackPanel. I put this adapted code into a short function at the top of your Playground. I didn’t go through and do all the styling required to get it to look exactly like what you had before, but it should be straightfoward enough for you to build on this to style the interface the way you want it. Hope this is helpful, and best of luck!