If you have watched Fate/Zero, you probably remember that Kiritsugu considered simply walking away from the Grail War, taking Iri and Illya with him, and destroying anyone standing in his way. Considering the way events unfolded from there onwards, it was a shame he didn't act on his promise... except the creators were so sorry for the man and his family that they created an officialFix Fic, in which he did exactly that. He realized that the safety and happiness of his own child and wife was more important than any world peace pipe dream, saved Illya from the Einzbern castle and stopped the Holy Grail War in its tracks. Since he and Irisviel are actively working to ensure that the War never happens again, not only can their family enjoy the stability and happiness they deserve, but Kiritsugu also achieved what he wanted all along: making the world itself a better place.
The scenes of Iri and Illya together. We get to see how would the mother/daughter relationship be without all the baggage of the main Fate 'verse, and the answer is apparently "Crazy Awesome". Iri travels home on the whim that something feels off with her daughter. She decides to rope Luvia and Rin into helping her spy on her daughters, probably well knowing that Kuro would notice it and uses it as an opportunity to bond with her in a moment so heartwarming your ventricles will melt.
Illya convincing Kuro to not give up and try her hardest to live.
An even bigger moment involving the two is when Bazett invades Luvia's mansion and begins fighting Luvia. Rin is watching from the shadows, sees how strong Bazett is, and has the opportunity to back out and escape. Instead, she stays and actually saves Luvia from being strangled by Bazett later on in the battle. For all their arguing, Rin and Luvia clearly have each other's back whenever it matters the most.
Illya and Miyu. Their relationship is adorable, starting with Miyu asking Illya how to fly and Illya's delight at her opening up.
Illya and Kuro's relationship as sisters. And the friendship between all three of them.
It's sweet to see poor Illya finally able to live a happy, peaceful life with her parents and Shirou as her older brother.
#23 has a small one: Miyu finally reuniting with her big brother. Also the love this version of Shirou have for Miyu - his sister: The guy is willing to take on all evils of the world if it means saving his sister
Later during Shirou's flashback, it's shown how he grew so close to his adoptive sister and why he's willing to go through hell and back in order to ensure her happiness.
Child Gil and Illya's friendship in 3wei. They get along so well, even though Gilgamesh rips out Illyasviel's heart in FSN it makes everything all the more cute and touching.
In Miyu's universe, the love that Sakura had for Shirou is very genuine and she was willing to throw everything away if it meant staying by her beloved Sempai's side. Which makes her death at Shinji's hands and later revival/brainwashing by Julian all the more tragic.
The reason Miyu's brother gives for saving his little sister.
"I'm an older brother. So I have to protect my younger sister, don't I?"
Chapter 41 reveals, for the last 400 years that Miyu's family only wished for their child to be born healthy. They could have made a wish at any time for wealth or riches, but only wanted their children to be well. With that knowledge, Shirou's actions are carrying out exactly what they would want.
Chapter 42 and 43 shows that Shirou finally reaches Miyu and with the omnipotent power of the Grail, wishes for his little sister to escape the evil clutches of the Ainsworths and leave their dying world; to travel to a place where she can make friends her age and finally be happy. While all this is happening, Shirou uses the last of his strength and endurance to challenge a Gilgamesh powered Angelica to a standstill and succeeds in rescuing Miyu. With Shirou's story finally coming to a close, everyone who is listening to it is in tears. Illya then thanks Shirou for essentially baring his heart and soul to them and is grateful towards the young hero who risked everything for the sake of one person. The closing caption sells it:
The boy fought with everything on the line, all to protect the girl's smile...