Word for a given situation

You could use the word "protocol". Then you could say you implemented the "Bear-Sneaker Protocol". Similar words would be "program" or "procedure".

Edit: Maneuver, like the Picard Maneuver.

I would call this the "Bear-Sneaker Stratagem". "Stratagem" is defined by Merriam-Webster as "a trick or plan for deceiving an enemy or for achieving a goal". If you want a less military-sounding context, "strategy" might work as well.

A similar term is "gambit", defined by Merriam-Webster as "something done or said in order to gain an advantage or to produce a desired result".

Sounds like you're looking for ploy.

a cunning plan or action designed to turn a situation to one's own advantage

In the original joke, one friend sacrificed another to avoid confrontation.

The way I read your story is that both you and your wife participated in the conflict until the bear, your daughter, left the conflict location. If you had left the room so that your wife had to deal with the bear, I would say that you had, at that point, enacted the "Bear-sneaker_______".

But, you didn't leave the area first, you simply survived the attack with a little sense of humor in tact, while your wife went mental. I would say your struggle did not meet the criteria of the "Bear-sneaker ________" because it does not follow the format of the joke, based on immediately leaving the scene first because the bear attack was imminent.

So you didn't really enact the "bear-sneaker _______", but you can brag to your wife that you "survived the bear attack", meaning you were less frustrated, more patient and lived to chuckle about it. This adds a new dimension or secondary context to your newly-created inside joke between you and your lovely wife.

In the future, when you find yourself leaving the area to avoid confrontation with the bear, then you could warn your unsuspecting spouse, using the terminology, "Bear-sneaker _________" because it follows the original format of the joke.

To maintain the upbeat nature of the inside joke and to keep it light and emotionally fluffy, I would call it the 'Bear-Sneaker Scramble"

trope noun \ˈtrōp\ –MW

b: a common or overused theme or device : cliché

Aww, not the Bear-Sneakers-Trope again...