Is there a technique to demonstrate the rational failure of logical fallacies?

I'm having a conversation with a group of people and they have accumulated 4 different fallacies as their attempts to counter my argument. I want to demonstrate how utterly bad their thinking is by swapping out me and my argument with someone else and their argument, then apply their fallacies to that argument. Unless they are completely clueless, they will see how their reasoning does not at all address the content of either argument and results in some pretty bad decisions. I thought this was a Reductio ad Absurdum, but realized that it's not.

What is this technique called?

I think that form of argumentation is a combination of analogy (because it's applied to something else that shares the analogy's critical element) and reductio ad absurdum . Fallacious attempts that fail to do that in a reasonable way result to weak analogy .   

I wrote about this calling it the Reductio Ad Consequentia. See my post at https://www.hostingauthors.com/posts/bobennett/reductio_ad_consequentia___reducing_the_argument_to_the_consequences.html .

This is what you wrote:

"I want to demonstrate how utterly bad their thinking is by swapping out me and my argument with someone else and their argument, then apply their fallacies to that argument."

I think this is your concern:
1. you swap out yourself so that your opponents have some kind of veil of ignorance. Like avoiding biases because of the person they're contending with.
2. you swap the argument with another argument that's similar to yours but perhaps easier to understand or to relate to. By "similar" we mean logically equivalent or in a way that if the fallacies apply to your argument, they should also apply to the swapped argument.

If you agree with what I understood, then let's produce an example.

Example: 
Timmy's mom: Timmy, if you don't do your homework, you will not pass your exam.
Timmy: But mom! I want to play video games. Besides, you're committing a slippery slope fallacy. Just because I don't do my homework, that doesn't mean I will not pass my exam.
Timmy's mom: Your dad said the same thing. And also suppose that you're looking for a job and your coach tells you that if you don't prepare for your interview, you won't get the job. Will your coach be committing a slippery slope?

In the example, Timmy's mom switched the person to Timmy's dad so that Timmy can avoid pre-conceived biases (like "my mom doesn't understand!") and switches the scenario in such a way that the advice given is somewhat similar to a point she's getting across (lack of responsibility implies less success).

If you agree with how I understood you, then I think this is technically not a reductio ad absurdum because I think that's a method to prove something by contradiction. What I think you're doing here is that you're actually accusing your opponents of a variation of special pleading. This is because maybe you're supposing that if they got a different scenario with different people, they wouldn't use the same standards on them as they are doing to you. Or perhaps they are not spotting what they're doing.