Intentionally committing hypocrisy, to show a wrong-doer why you think what they do is wrong

Not a single word but an idiom for your consideration...

give somebody a dose/taste of their own medicine

to do the same bad thing to someone that they have often done to you, in order to show them how unpleasant it is She's always turning up late for me so I thought I'd give her a taste of her own medicine and see how she likes it. -- Cambridge Idioms Dictionary, 2nd ed.

What you describe is tit for tat (Merriam-Webster):

: an equivalent given in return (as for an injury) : retaliation in kind

Oxford Learner’s Dictionaries gives good examples:

a situation in which you do something bad to someone because they have done the same to you

● the routine tit for tat when countries expel each other's envoys

● tit-for-tat assassinations by rival gangs

Especially in game theory, which is used in various academic fields, tit for tat is the name given to a strategy where you’re nice to the other if they’re nice to you, and bad if they’re bad, with the aim of ensuring that you’re both nice to each other. The Wikipedia article has some more details.

And your attitude is not hypocrisy. If you preached the virtue of giving the other cheek and then retaliated you’d be hypocritical. But if you say, look, we should both clean up after using the kitchen, but if you live it in a big mess for me then I’ll leave it in a big mess for you, that’s not hypocrisy, it’s tit for tat.

In a comment (which the OP asked to be made into an answer), I wrote:

It is hypocrisy, but turnabout is fair play.

In this comment, I suggest the action of retaliation could be called a turnabout, and it actually has such a definition:

: an act or instance of retaliating <turnabout is fair play>
_{Merriam-Webster}

The phrase is an idiom, and one of its uses is:

Prov. It is fair for one to suffer whatever one has caused others to suffer.
So, you don't like being made fun of! Well, turnabout is fair play.
_{The Free Dictonary by Farlex}

The term payback is often used

An act of revenge or retaliation: the drive-by shootings are mainly paybacks

The phrase payback is a bitch is often used to focus on the satisfaction of the responder in making the original offender uncomfortable.

Note that the term does not necessarily imply that the person engaging in payback is acting against his own values or inclinations.

Also, when the response is more extensive than the original offending act, the term escalation may be used

An increase in the intensity or seriousness of something; an intensification: an escalation of violence

Oxford Dictionaries Online