What makes you think you need to convert CMYK to RGB for any purpose?
You can display a PDF file with CMYK colors without any issue.
You can add swatches from either RGB or CMYK to the swatches panel.
If I open a new document with Digital checked in Setup, it works. But how do I change it in an existing one?
It sounds like you have transparency on some or all of your spreads and your Transparency Blend Space is set to CMYK—by default new documents with a Digital Publishing Intent will start with all RGB swatches and an RGB blend space, which would explain why new docs are working for you. Try changing Edit>Transparency Blend Space to Document RGB and leave Overprint Preview and Proof Colors turned off.
When you export you can convert all color to a single RGB color space like this: