My view of this is that they _don't_ want to become a part of the republic unless they are the ones who calls the shots via an invasion. They are very proud to be Mandalorians and their aim is to take back what they lost in the war against Revan. But, as HK 47 says if you get him on your side, their cause is already lost since too much was lost to Revan...
Still, being Mandalorians, or at least an ambitious Mandalorian, the goal is none the less to make the Mandalorians a force in the universe again (no pun intended) ;-).