Hello Nicole: I recall having replied to your previous post.

I have something similar to what you describe that has gone on with me for many years. There's the me I present to the world.

It's not as nice or as positive as it sounds like your external persona is.

But it's not violent either.

Then there's the other "internal" part of my persona. It is very similar to your p2... plus I will add deeply confused & conflicted.

I have sometimes worried that if that other part of my persona were ever to escape, it's hard to know what type of damage it might do!

(I'm pretty confident that's not going to happen...)
You mention, in your post, that you've sought help with your ongoing depression. I don't know what type of help this is. Hopefully, you're seeing a therapist & you've been able to delve into that darker aspect of your personality with your T. Or if you have not gotten to that yet, hopefully you will feel able to do so soon. Therapy is really the way to sort through these aspects of one's psyche
I presume we all have this kind of "dual personality" within us. Perhaps it is more pronounced in some of us than it is in others. I don't know.

I know it has sometimes felt pretty intense for me. In my case, the way I have chosen to address what I experience is through the use of Buddhist practices that emphasize acceptance of one's demons with compassion. And this seems to be working for me. But for the majority of people, I presume, therapy is going to be the more appropriate approach. I wish you well...