Maybe this should have been more explicit in the docs, sorry. The reason we're not shipping any database drivers with Prodigy is that there are too many options and user preferences – we want to keep the dependencies lightweight, instead of making the user install all database drivers by default. In theory, you can even plug in your very own database solution by adding your own Database class, so Prodigy tries to not many too many assumptions about the user's preference here.
The thread I linked above should include all relevant details on remove connections – including the code snippet contributed by a fellow Prodigy user. Essentially, Prodigy's built-in Database class can be initialised with any valid peewee database, however you choose to construct it. Here's a StackOverflow thread on remote MySQL databases with peewee. There's also the Playhouse extension which adds even more advanced functionality – but I'm not sure if this is relevant in your case.
The easiest way for now is probably to try it out with one of the MySQL Python drivers and make sure it all works as expected.