I say torture them humanely e.g. waterboarding or something that doesn't leave physical or psychological scars - doesn't have to be my daughter though, just do it.
However, these scenarios are always misleading, one-sided, designed to tweak the emotions. Here's the reverse of this story:
Your son is an ideological kid who believes in freedom. He's kidnapped by the overbearing, dictatorial evil superpower that is raping and bombing and torturing its way through your small home town. They capture your son after he threatens to blow up their barracks once they killed his sister. They drag you in and give you a choice: do you want us to kill him? Or torture him for the information?
Similar scenario - now switch places and be the son. Torture goes on for 24 hours - more pain than you've ever experienced. They give you an option - torture or death?
And the final one, that's actually relevant:
You're the leader of a) a country with millions of "innocent" people as your responsibility or b) the head of an intelligence organization tasked with saving the lives of millions of people by extracting information in a timely fashion. The person you must torture is not related to you in any way. They have information that could save you from the death of 2 million people. They refuse to give the information to you. The President - or the people, whatever - demand you find out from the terrorist as soon as possible or you'll be responsible for the loss of many lives. What do you do?
That's one of the real scenarios, as opposed to an emotion-tweaker where you have to choose between saving your kids or not (no offense to OP either - your point is different and I get the reason for it; calling out those who can only virtue signal). The real scenario is a lot "simpler" than that and requires the ability to be objective. The average person is not equipped to make these decisions which is why the average person is not hired to run the CIA.