I'm asking about montages of some criminal or depressing thing that have a happy song underneath them. The first show I remember seeing them on is Breaking Bad, but I've also seen them on Stranger Things and probably other shows. Where do they come from?
You may be looking at a Sad Times Montage
A sequence in which it is shown that, while time is passing, the protagonist is feeling sad and alone. Opposite of the Good-Times Montage. In fact, some films will juxtapose a Sad-Times Montage with a Good-Times Montage earlier in the film, only with different music.
The description is very general but provides a more specific example
A montage appears in Good Morning, Vietnam, with images of American war atrocities played against, again, "What a Wonderful World".
Soundtrack Dissonance is utilized to, in literary terms, pose a juxtaposition with the intent of making a thematic statement and/or widening our emotional distance to the events before us, thus allowing us to view the piece in a more removed, intellectual manner.
You're taking advantage of a tactic used countless times over the years to heighten the sadness of a scene. Your dissonant music doesn't have to be played over a violent scene, of course. Happy, upbeat music at a funeral of a beloved character can also work. It can be used to excellent effect, especially if the song is somewhat silly