I don't think the people of the Core Worlds are exactly recruitable... have you played Alderaan? Those pompous nobles would never become Mandalorian. Most likely their would be resistance on every world, and lets face it. The option in which the Jedi never intervene is impossible. I mean, when they finally reach Coruscant the Jedi Council aren't just going to meditate and let the Mandorians shoot them in their chamber :P
Sure the Republic would be heavily, heavily outnumbered. But I believe the Mandalorians would fall apart, fighting amongst themselves for the galaxy they have pillaged and wipe each other out - this would make the Republic's job a lot easier.
No they aren't. So they Mandalorians would just bombard the world into submission. And this scenario is if the Jedi had completely abstained from the war.
I don't think the Mandalorians would turn on each other. Mandalore the Ultimate was one of the greatest Mandalorian leaders. He united the clans for a single purpose. They were united in the fact that they wanted a glorious victory. They wouldn't jeapordize that.
We also have to remember that Republic morale, numbers and supplies have run low. By the time the Mandalorians hit the Core Worlds, they have taken control of vital trade routes, gained multiple victories against Republic forces, and just the fact that they were in the Core would give a sense of hopelessness to the people.