How to prove ourselve & capability of work in any kind of situation, if we have in our Management 2 or more Directors?

By doing the assigned tasks as instructed and by the books, be willing to take more responsibility, be a positive workforce in the organization, and stay away from gossip and non-sense. 

Considering the fact that i am very junior to you, I would like to apologize in advance if I make a wrong statement. Generally where the organizations have two or more directors there is a lobby followed by a division of the workforce. Most of the people succumb to this and tend to outsmart the others by finding faults in their work rather than focusing on their own efforts. This approach has a few positives and a lot of negatives as sooner or later you get what you have given. Hence the best possible way is to focus on your work and acquire new skills. This helps one to outsmart others and strive in the long run.