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.
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 loves 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.