I checked, and it does not seem the Republic or CIS can build Corellian ships EXCEPT for the corvette. As for Mandalorion ships... I could not find any direct info, but I did notice that there is a space defense over Mandalore. I would suggest that you use Padme (if you're Republic) to get the planet to join so you don't destroy the structure, then try to build ships. If you're CIS, however, I'm not sure you can capture Mandalore without destroying the space structure, so it's likely not possible with that faction.

Thanks for the info, maybe someone can make a submod for it, would do it myself but have no idea how.