Oh no, what a dilemma. I'm so sorry for your problem. And poor Bassett too.

I agree with the others that a helpful solution may be to medicate Nutmeg, or another thought.....maybe get a separate litter box for Bassett? You may already have thought of this, but it's the only other thing I could think of. Maybe part of the reason Nutmeg is hounding Bassett is cause she doesn't want to share....

Good Luck!