Is it permissible to take the difference in price between what the sister pays and what can be saved through the contractor's expertise in supervising the construction of her building?

If the purchase of building materials is part of the supervision of the construction, then you are not permitted to keep the difference in prices for yourself, because you are an agent for your sister, and any increase obtained by an agent belongs to their principal. However, if the purchase is not included in the supervision, then it is permissible to agree with your sister or the contractor that you buy the materials at a certain price, and the difference will be yours if you buy them at a lower price, as in the Hadith of Ibn Abbas: "There is no harm in saying: Sell this garment, and whatever exceeds such-and-such amount is yours." It is also permissible to agree to take money in exchange for guiding to someone who sells at lower prices, which is known as brokerage, provided that it is known and by prior agreement.