Your girlfriend has a good idea. I don't think it will cause too much stress. Brisco and Golley are half brothers and they have spent their whole lifes together in a pasture, together on trails, together on everything. This year they got to be separated in their pasture and they did quite well. Brisco and Golley have been separated on trails before, and they have done very nicely.
One thing you could try, is slow separation rather than drastic - if you are worried about having their minds blown. (And this might be a better option in this case.)
Take both horses out to the arena and tie on to the fence. Work the other horse close to the tied mare. Lets call the tied mare 1 and the mare you are working with mare 2.
The next day, Tie mare 1 further down the fence. Work with mare 2 in the same spot you did yesterday.
Next day, mare 1 even further down and work with mare 2 in the same area.
Etc. Until mare 1 is all the way to the other end of the arena.
Then tie the mare 1 somewhere outside the arena, but where they can still see each other. Work mare 2 wherever - making sure that a few times that mare gets out of sight with mare1.
Eventually, you will be able to first keep mare 1 in a stall and be OK and then have the mare keep in the arena while you work with your mare.
If the mare in the pasture still continues to whinny, that is fine. Over time she will learn that whinnying won't do anything.
When you work with your mare, in the warming up process make sure to groundwork her a lot and make sure to do a bunch of different cues so she takes her mind off the other mare and more on you. Each time you are working with her, if she begins to act up, do tons of groundwork or riding exercises to take her mind off the mare.
You also might want to do what your girlfriend says once the mare 1 can be int eh stall and far away from mare2. Just separate them for a few weeks or months and then put them together and if they act up again, separate them, but this time you won't have to worry about "blowing their minds."
🔫 Don't Tread On Me 🐍