If you are only using camera raw in that you do not use photoshop afterwards for other touchups, etc. you can save a jpg directly in camera raw.
The only time the save as a copy should be mark by default is when the original image is of the same format. Thats to make sure you do not overwrite the original image. If it is doing this when opening/placing a different format, then perhaps the preferences are corrupted. (guessing)
As for other ways to save as a jpg from a raw file, you can use the batch command or image processor command (I prefer the latter) as it can bypass camera raw altogether when converting a raw file to a jpg. And do a whole folder to once.
You could also use save for web and devices.
one can't have 2 files with the same name in the same folder. Save the edited jpg to another folder. Then you will have both. Of course, they will be in different folders.
I assume you use features that are not viable in jpg (like Layers for example).
But starting with a jpg if the uncompressed data ia actually available seems a bad idea to me, as does discarding the layered file and only keeping a flattened one, especially with destructive compression being applied multiple times.