New twist on 2 weapon fighting, adding a 3rd weapon (magical)

I have three weapons:

rapier

dagger

Dancing Weapon (magical)

I attack with a rapier then because of the Nick property I attack with the dagger.  My bonus action is an attack with the Dancing weapon .

Is that correct?  Do I need nick mastery to be able to use Nick?

On the 4th turn when the dancing weapon comes back, Can I use the rapier/dagger combo then sheath the dagger, and catch the dancing weapon?

Quote from Character77006 >>

I have three weapons:

rapier

dagger

Dancing Weapon (magical)

I attack with a rapier then because of the Nick property I attack with the dagger.  My bonus action is an attack with the Dancing weapon .

Is that correct?  

No. Nick modifies the extra attack you get from the Light property, so both weapons need to be Light. The Rapier is not. This would work if you were using a Shortsword (or some other Light weapon) instead of the Rapier, though.

Quote from Character77006 >>

 Do I need nick mastery to be able to use Nick? 

Yes. You can't use class features you don't have.

Quote from Character77006 >>

On the 4th turn when the dancing weapon comes back, Can I use the rapier/dagger combo then sheath the dagger, and catch the dancing weapon? 

I don't see why not (again assuming you use a Light weapon instead of the Rapier).

Thank you