It's absolutely a scam, and not even a very complex one. The guy impersonates an attractive woman in her early 20's, gets you to send nudes, then plays the "angry father". If that doesn't work, his accomplice plays the "detective" to add authority, fear, and urgency.

First clue: the "angry father" is demanding money. That's not what fathers do when they find out a 20-something is sending naked pictures to their 15 year old daughter. A real father would probably demand you delete the photos and don't contact his daughter, or just threaten to kill the ever living fuck out of you.

Second clue: the "detective" is negotiating for you to pay money to the "angry father". It would have been more believable if they stuck with "give me money or I'll call the cops". Real police would either try to get a confession before you have an attorney present, or just explain they aren't pursuing charges because the "daughter" solicited the nude photos under the guise of an adult on an adult website.

Third clue: the "detective" hung up when you pressed for a badge number, indicated your intent to verify their identity, and informed them you're recording. Scammers want easy, gullible targets. If you push back in any way, they'll hang up and move on.

Bonus tip: In the U.S., you never have to inform a police officer you're recording them during the course of their official duties. You can't record in sensitive areas where recording devices are prohibited, but otherwise you can record the police doing police business and you don't have to tell them.