Mine is a bit niche. Male anti hero protagonist revenge movies. Usually takes place in england. Always has a heavy criminal element, a good bit of violence and the lead usually dies in the end. Recent favorites include “Bull” “Avengment” and “Villan”. Not sure if this specific type of movie is a genre or not but there’s plenty of them.
Gotta be found family movies, particularly if the parental figure didn’t want the responsibility in the first place or if they’re clueless, gruff, and/or emotionally not prepared for a child.
So movies like Logan, Ice Age, Wild Robot, Up, or Despicable Me and shows like The Last of Us, The Mandalorian, Game of Thrones (Arya and the Hound), and The Witcher.
I was trying to think of more found family mother shows and movies and honestly couldn’t think of more. Most of the ones involving women that I could find are of friend groups or there was no hesitation to pretty much adopt the child.
Try a French classic from the 80s, Three Men and a Cradle (3 hommes et un couffin). Maybe not exactly the same, but similar enough that you might find it fun.
Found family, never somethjng I really considered to be a genre. You’re absolutely right though and I do love that kind of story.