I can’t remember the exact reasons, but I’m pretty sure that it’s not possible to share a single site in development and production. I believe it has to do with the fact that Discovery also makes use of the internal URL to access the LMS externally, e.g: from the browser.
Also, the reason why we use the production site even in dev is probably that it’s the only one that works correctly in both cases – but I’m sure, to be honest.
If you can find a (tested) solution that is guaranteed to work in dev and prod I’m all ears. Discovery sites have always been a huge PITA for me.