while they get to show them off
Show them off to whom? This whole thing sounds completely crazy.
Quite a few of us on this thread have clearly been to inaugural lectures at which children are, up to a point, welcome. So let's assume it's that. Even so, how does "hello, I'm the new professor's mother, these are my grandchildren, I know, the new professor doesn't have any, these are the children of the new professor's brother and his wife" play out? What's the audience that won't think the mother is unhinged?
You can construct some complex psychological model in which the mother is upset that her daughter, the new professor, does not have children and wants to give the impression that she does, in fact, have children, but surely that's the stuff of /r/JustNoMil made-up troll fantasy nonsense, not reality?
And if it's not an inaugural lecture (the OP hasn't said, as is entirely her right) then the children aren't welcome anyway, so it's all rather moot.
My initial assumption is that this is golden sister, scapegoat brother, but even in that context, it's incomprehensible.
I'm not one for the immediate screams of "No Contact!" but this all sounds so deranged that a long time-out while mother in law gets her shit together might not be a bad idea.