About the song Hana no Haru / ハナの春, there are conflicting sources as to whether this song appears in the anime or not.
Anison.info and Anidb say it's a song image:
http://anison.info/data/program/2819.html
https://anidb.net/anime/4726
But the movie's official website or the vinyl single say it's a theme song:
http://www.mushi-pro.co.jp/2010/08/%E3%82%86%E3%81%8D/
https://vgmdb.net/db/covers.php?do=view&cover=384858
So I watched the anime on Youtube to find out, and this song does not appear in the anime, so Anison.info is right. We can hear the opening theme "Yuki" 5 minutes from the start, and the songs "Yume no Mukatte" and "Itsushika Ai wa" towards the end of the film, but no 4th song.
I was also able to verify the names of the songs appearing in the anime, as they were released on CD in the album Sumiko "Rarities", and we can therefore listen to samples, especially on this site :
https://www.hmv.co.jp/en/artist_%E3%...-Songs_5390894
Also I don't know if anyone might be interested here, but this obscure anime was released this year in France on DVD and Blu-Ray (with Japanese and French languages), and you can buy it on Amazon:
https://www.amazon.fr/Yuki-Secret-Mo.../dp/B08KWQ385B