Zouken Matou never meant for Sakura to take a part in any Holy Grail War. His initial plan was to train Sakura into a tough mage. He would then let her give birth to (probably with Shinji) the next heir of the Matous, who would fight in the next war. As Kiritsugu did not make a wish in the fourth war, the energy was almost unconsumed. As a result, the Greater Grail only spent only 10 years restoring the energy for the fifth war instead of the expected 60 years, which neither Kiritsugu (who planned to destroy the Greater Grail in around 20 years) nor Zouken had foreseen.
Zouken thought it would be a waste to not summon a Servant if they had the chance. He thus made Sakura do her summoning, although he did not take it seriously: he still wanted to keep his original plan. Zouken did not care about the fifth war or about the actions of his grandchildren. As a result, eager to prove his own ability, Shinji participated in the war since Sakura herself didn't want to participate, by forcing Sakura to give him the Book of False Attendant and Rider.
In the Fate route, Sakura was depressed when her brother disappeared from the town, as he had been killed during the 5th Holy Grail War (something Sakura herself may have been aware of). (Although Shinji was a complete jerk, Sakura held some strange feelings for him; she actually pitied him not being a mage and thought she somehow had to "protect" her "poor" brother.). But since Illya was alive and stayed at Taiga's house, visiting Shirou very often in this route, they became good friends and Illya always cheered her up, making Sakura regain her energy quickly.
In the Unlimited Blade Works route, Shinji was still alive, and stayed in the hospital for a couple of days after Rin saved him. Sakura insisted on taking care of him during his hospitalisation, and they seemed to "get along better than before" from Shirou's view. It was stated that after this lesson, Shinji gave up on being a mage, so he would treat Sakura a little better than before, although his arrogance did not change and he had a happy life from then on. Since Sakura still didn't want to stop pitying on and looking after her poor big brother, she would likely live the rest of her life in Matou residence with Shinji.
Although Sakura loved Shirou more than anybody else in the world, she thought herself too "filthy" for someone as good as him (which is another reason she cares about Shinji, as she thought they were both kids "abandoned" in the dark). As a result, she always stayed away and wished a girl good enough for Shirou appear. She let Shirou love Saber for the rest of his life in the Fate route and Rin take Shirou away to London in Unlimited Blade Works, which is really cruel as she had always envied her for living a happy, perfect life.
Moreover, no one in the Matou household ever cared about Sakura, other than Shinji, when he still thought Sakura was forced to leave her family and unlike him, had no chance to learn magic. He occasionally looked after her out of pity until he found out that in fact Sakura was the one who was going to inherit the Matou line and who always took pity on him. But even Shinji only abused his sister later on, this was the only kind of attention Sakura could get from the whole Matou family. Thus, she did somehow cherish Shinji as her big brother. She thought him to be pitiable enough that even when he beat her she had to beg Shirou not to blame him, as Shirou was Shinji's only friend.
Aside from the Heaven's Feel route, where he activated another of his plans for Sakura and the Grail, Zouken would have had to accept that his wish for immortality could never come true. Rin and Waver dismantled the Greater Grail a decade later, and Zouken would be weak enough at the point in Fate/hollow ataraxia (though kind of a joke, that's still canon in the Type Moon universe) that Sakura viewed him as a old man who was nearly dead. (So yes, in F/HA, Sakura did take over the household and rule over Shinji and Zouken, who were frightened to death.)
Even in the original story, in the two routes, Fate and Unlimited Blade Works, Zouken would die soon and so Sakura would be free, and the only problem would be whether she would still follow Zouken's wish to have children with Shinji.