Is there a verb for unintentionally showing your rear end?

A one-word verb that fits would be to plumber-butt.

According to Wikipedia:

The terms plumber butt or plumber's crack (Canadian, Australian and American English) and builder's bum (British English) refer to the exposure of male buttock cleavage, especially on occasions of careless bending over.

While usually it's "plumber's butt" (noun), a verb plumber-butt also exists, according to Google:

When you put on your pants, is the band of your underwear above the top of your pants or are you just plumber-butting all over the place?

If you're bending over to stretch, you should be confident that you won't be plumber-butting the cardio wing. (in a gym.)

Evidently plumber-butting is mostly unintentional. It is certainly no mooning.

Regarding your examples:

"Hey, you both are plumber-butting everyone behind you."

The second one is trickier and needs some rephrasing, perhaps:

"Ugh, the plumber was in the kitchen and, you know, did what the plumbers do: he plumber-butted me while I was eating."

Or simply:

"Ugh, the plumber was in the kitchen, plumber-butting me while I was eating."