Is their a name for the argument that goes something like: “Would you feel the same about the death penalty if someone killed your kid?”
Appeal to emotion?
I thik that’s a form of ad hominem, which tries to get a person to agree with a position based on his or her personal (even if hypothetical) circumstances.
A veiled threat?
That’s not an argument, so it can’t be fallacious. It’s a question. There are multiple ways to restate it as an argument, which are fallacious, but in different ways.
“If someone killed your kid, then you would oppose the death penalty” is perhaps an appeal to pity.
“Anyone who has lost a child knows the death penalty is wrong!” is a generalization.