It’s so easy when you want to create a rectangle with rounded corners in Adobe Illustrator to just click that Rounded Rectangle tool icon in the Tools panel and just click & drag. The problem is, you have no control over those corners once your rectangle is created.
Sure, you could select the Rounded Rectangle tool icon and Option + click to bring up a dialog box allowing you to specify the radius of the corners. But again, once the rectangle is dragged out, that’s it. There’s no going back and changing that radius later, and attempts to resize the rectangle later on actually resizes or stretches the rounded corners.
Illustrator's rounded rectangle tool isn't the best way to create rounded corners
If you want to keep full control over those rounded corners of your rectangle, use the normal squared-edge Rectangle tool icon in the Tools panel. Once your rectangle is dragged out on the page, go to Effect>Stylize>Round Corners… in the menubar.
In the dialog box that appears, you can specify a custom corner radius amount. And here’s the great part. This is an effect applied to the rectangle, not the actual rectangle path.
Illustrator's Rounded Corner Effect offers more flexibility with rounded corners
So now when you stretch that original three inch wide rectangle to nine inches wide, the corner radius doesn’t stretch with it, it stays exactly at the amount you specified. As an added bonus, you can go back later and change that radius amount if you wish via a quick visit to the Appearance panel.