Used car sales are presumed to be "as is" sales in the State of Washington. She cannot force the cancellation of the sale unless she can prove you made a material (important) false statement about the car. Sounds like despite doing her due diligence, the car still has a problem. It is now her problem.
If you were to negotiate a resolution, include as a condition of your payment that she must sign a mutual full release of all claims known or unknown. However, unless you made a material misrepresentation about the car (or if there are others facts not disclosed here for consideration that I do not know about) then I would not be inclined to negotiate about this.
A known risk of buying any private party used auto is that it could break the next day.