First the rationale:
That quote in the Javadoc is a bit... weird. If you understand "running" as being between onResume() and onPause(), then normally two Activities belonging to the same Application cannot "run simultaneously". You would probably have to mess with the Application class or the OS itself to have it behave otherwise.
To wit, I'm actually developing an app at the moment that uses several MapActivity subclasses and haven't encountered any problems so far (i.e. 40+h of development and testing, both on emulators and a device).
Therefore I would suggest:
- Try to implement your app as a single-process activity with a local service and just run with it.
- If you don't want to do that (can't blame you ;) ), or you encounter any problems, I would suggest starting out with a MapView, perhaps encapsulated within a Fragment. Here's a discussion to get you started.
In short, due to Android's practical fragmentation, keeping your Activities in one process and commiting more time by starting with a more bare-bones implementation will be a safer, ultimately less time-consuming and probably more efficient approach than artificially splitting your app and potentially gritting your teeth on the IPC. At least in my opinion.