There’s not a way as of yet to run multiple dash applications from a notebook (or even, to perform other operations within your notebook if you’re running the app from that notebook.) You correctly guessed the reason as well, the kernel is busy running the dash app and can’t do anything else.
One workaround is to try a version of this solution: Can I run dash app in jupyter
Iframes will work no matter where the app is running from, so just run the app from the terminal and display it in your notebook.