Is it permissible to take money from a place where the questioner works and give it to his aunt, whose husband does not provide for her, knowing that the money does not belong to her husband but to his cousin, and is that considered a breach of trust?

It is not permissible to take money without the owner's permission, and this is an act of treachery forbidden by Islamic law. You must repent and return what you have taken, even if through indirect means, because "the hand is responsible for what it takes until it returns it." Your aunt is also entrusted with her husband's money, and it is not permissible for her to take anything unless he withholds the obligatory maintenance from her, in which case she may take what is reasonable.