“The house isn't being sold” – but her half IS being sold. “A form 1099-S shouldn't be sent since it's not a sale” – who made up that rule, you or the title company?

She is selling her half of the house. The fact that the buyer owns the other half, is irrelevant. At least you acknowledge there is a buyer.  A transaction with a buyer but no seller is like the sound of one hand clapping. 

However, at least one reliable source cites authority that she can claim the $250K exclusion. See

https://www.thetaxadviser.com/issues/2017/apr/tax-issues-nontraditional-households.html