Note: This first paragraph is spoiler free.
Swimming Pool is about the author Sarah Morton played by Charlotte Rampling, and her run in with the daughter of her publisher named Julie played by Ludivine Sagnier, while Sarah stays are her publishers house to get settled into to writing a new book. Rampling is terrific as a secluded author who finds both disgust and intrigue into Julie. Sagnier is decent as the publishers wild daughter who is promiscuous and is defensive against a scolding Sarah. Eventually they come together, even finding things they have in common, on the way toward Sarah helping Julie out after something terrible happens. Sarah's main motive in all of this seems to be to write a book, but there's authentic interest, especially in her stares on Julie which neither seem scolding nor approving. I liked the dynamic between the two characters, even as a certain major event seems quite unlikely.
SPOILER SPOILER SPOILERS BELLOW The movie ends with an extraordinary twist and I think I understand it. I will say this twist didn't make me like the movie more, and may of even made me like it less, but whatever one thinks about it it certainly is different. You can't compare the twist to The Sixth Sense or Fight Club, or The Crying Game, and so on, because those twists made you simply look at events in a different light; they did not change what had actually occurred (though I guess Fight Club did change events to an extent). My theory is this. The real daughter Julia actually stayed with her, but the movie was representing her imagination of a more attractive and delinquent daughter named Julie. At the end Sarah says to her publisher that there were things he kept from her, and that was one of the reasons she decided to go to another publisher; something she found out was hidden from her, and the real daughter could be that. The cross replacement thing would make sense with a Julia as she would far more likely be religious than someone like Julie. The theory of Julie being a real illegitimate daughter of another mother has one flaw, almost fatal, and that's she does not look surprised at the end when she see's Julia and her father. That makes it seem that either she never met one of his daughters, or did in fact meet that one. And just an imagination Julie and nothing else does not explain what she meant by her publisher hiding things from her. Also the very end with the wave sequences of both Julia and Julie shows the first as it really happened, and the second as she imagined it. I can't say this theory is certain, and maybe there's no one certain answer, but I think it holds water more than the others.