"My Wife or Mom is kidnapped; you HAVE to let me lead the investigation."

I really doubt the competence of a cop who can’t even tell if it’s his wife or his mom who was kidnapped.

There’s an ok 80’s buddy cop movie, Shoot to Kill with Sidney Poitier and Tom Berenger, where the opposite happens. The bad guy is threatening to shoot a woman unless Sidney Poitier’s character drops his gun. Mr. Poitier states that the only way the killer is getting out of this alive is if he drops his gun immediately. Bad guy doesn’t, gets shot. That scene has stuck in my mind as the only time I’ve seen this scenario subverted.

The scene in very bad quality.

That’s kinda the joke in Lethal Weapon 4, where they get promoted to keep them off the streets.

Yup! Deep Space Nine had one.

48 Hours, as well. It is basically a trope itself.

Well, if it’s CSI: Alabama

Ha-ha! No, then it would be his wife or his cousin.