I've had a couple "moments" with my in-laws. Never with my wife's mother, a few times with her Aunt and a couple times with her father.
The times with her Aunt, it's never blown up into anything because of the way I've approached the situation. She tends to overstep her boundaries when it comes to my household functions (i.e. how my wife and I have decided to run our household). She's tried to insert her own ways and means into the fabric of our household to the point, a few times, where I've had to sternly tell her to cease. Generally, when I call her out on this, respectfully, she become contrite and obliges and everything is fine after that. Never anything past this.
The few times with my father-in-law: it's always just about his inconsistent political views. Never really anything malignant, he just gets very sensitive when our views differ to the point where he starts in with ad hominem attacks towards myself. I, then, tell him that we're getting off topic and change the conversation (nothing good will come of me retaliating in kind).
Like has been said, if there's a way to diplomatically resolve the situation, it will be your best bet long term. Especially if you can do so while maintaining the upper hand, yet not conceding to their bullshit. I wouldn't recommend approaching the situation emotionally. That tends to descend into a cluster fuck.
Good Luck .. this is shaky territory