Is it permissible for me to inform my aunt of my father's acceptance of her father's price to buy her share of the house, on condition that I pay her the remaining difference from the price she desires, without informing her female cousins of this, in order to avoid the family problems that would result from it?

May Allah reward you for your eagerness to resolve the dispute. There is no blame upon you for asking your aunt to conceal the matter. As for the remainder of the price that you have taken upon yourself, it falls under the category of commitment, and its ruling is that of a gift of reward (hibat al-thawab). Therefore, it is a debt upon you and would be taken from your estate should you die before fulfilling it.