I don't know what the backstory is here, but does LW seriously think the only two options are "blow everything up" and "seethe silently forever"? How about "attempt a reasonable conversation where you state that, overreaction or not, you just don't think that's a funny joke and don't want him sending that sort of thing to the kids"? And then, if that doesn't work, then you can blow up at him.

Or, I don't know, maybe BIL is a massive asshole and the rest of the family has always been a bunch of assholey enablers, in which case, great, LW, blow it all up, I'll hand you the matches.

(Without more context it is impossible to tell if LW is being oversensitive or not.)