Personally, I hate it when people separate horses semi-permanently/ permanently because they have separation anxiety. That’s exactly what they’re anxious over. When their friend leaves they have that “omg my best friend left me forever and I’m all by myself and if a lion comes, I’ll be all alone to defend myself!”
I also hate it when people just lunge/ roundpen the anxious parties to death. That’s not helping their anxiety, you’re just masking it by making them tired. Also the horse thinks being separated already sucks. If they have to run around I’m circles every time they’re separated they’re just going to think separation is even more terrible.
IME, separation anxiety kind of just goes away slowly over time. Every time the horses get reunited after being separated, they go “ok we didn’t die.” And eventually they get confident enough to be relaxed by themselves because they know life will go on and they’ll be reunited. So my first thought, would be ignore it.
If ignoring it isn’t working, I would separate them slowly and gradually. Maybe one day you pull one horse out for 5 minutes where they can still see each other then you put him back. Once you can do that you can go a little further/ longer. Also make their time apart fun for both. Maybe for the horse that’s stuck in the paddock, throw some hay and for the other one do some hand grazing.
It’s just important to remember separation anxiety is just that, an anxiety so it should be treated like one. You don’t punish them, you don’t mask it, you just need to be patient and understanding.