I think you are looking for a fanfic called The Mischievous Lady
The Mischievous Lady
AU. Sesshomaru needs a mate, and since he does not want to find one himself, his court decided to help him. They will call for noblewomen around the country to compete and become His Lady. All is politics for him but that is about to change. "You must be prepared, Sesshomaru. You are about to fall in love." Inu no Taisho warned him. He should've taken this warning seriously. [Full Summary Inside]
Rating:
MA
I love this story!!! I keep messaging the author to update. If you have time, show her some support and hope we can get an update!