Chicken with no flockmates depressed. Is it ok to just introduce one chicken?

[aart]

Welcome to BYC, sorry you're having troubles.

Depending on how 'firm' Dad is, you might explain that 2 is no different than 3.
Understand 'picking your battles tho'.

Mrs. K has given great advice.
Adding birds can be tricky....works best with 'extra' separate but adjacent space.
Knowing what your coop and run is like, dimensions and pics, would help us give you more specific advice as to how to integrate.

 

[Splendid Medley]

If you feel like she may be resistant to new birds try the same breed, either as she is, or to what your other 2 were.

I'm sorry for your loss. One of my hens was killed last summer by a dog (one of the girls in the pic). I had three originally, and when she died added two more from their former flock (luckily the original owner was willing to give me two more). Adding two was great because it gave them each a known companion while they adjusted. It took about a week for everyone to establish themselves in the new group dynamic.