@tetris7,
The answer is that she is batshit crazy.
Seriously, does it matter? She's an asshole your brother married. I'm sorry it's poisoned your relationship with your brother. But the remainder of your family seems to get that it's her and not you, yes? Then clear it up if that's not the case, but not in accusatory manner.
As in, tell your cousins (or whoever), "I didn't go to the mall on Sunday." (or whatever the wholly verifiable lie was). Not, "Margie (or whatever her name is) is a jerk for spreading lies about me." Just, address the untruth directly and refute it, nothing more.
This woman wants to create drama. Your job, after you've set the record straight, is to cut the drama off at its knees. But also, pick your battles. If it really is something as trivial as whether you went to the mall, then who the hell cares if she's lying about that? It's dumb but it's essentially harmless. If instead she's claiming that you said you'd go out to the woodshed and shoot your mother if you could find the time, well, that's a different story. Something that hostile really should be refuted.
I suspect your brother will begin to figure things out as I have every certainty that this bully who feeds on drama is pushing everyone else away. When he wakes up and his family is gone, and all he's left with is this shrew of a wife, he'll come to the realization.
I also want to add - if he is being physically abused (because this behavior seems as if it could be connected to psychological abuse), then do your best, with your family, to intervene. Yes, men can be physically abused by their wives. It does happen.