You need to move the stalls so they aren’t near each other and also should shut one in while the other one comes and goes. No shared turnout and no next to each other.
I stumbled across these videos one day and think some are quite helpful. There are some on separation anxiety which he fixes by groundwork.
I struggled with this for two years, I tried separation and riding my mare through it. Quite frankly nothing worked, some horses just never “get over” it. I was unhappy and so was she. I tried adding another horse but she was just as attached to that one, maybe worse. I ended up boarding her and she was happy and being able to enjoy my horse again was worth every penny.
If it is absolutely impossible to move them to unadjoining stalls, the mini could help. I have a similar situation at home: the two horses are in adjoining stalls and paddocks and one gets a little hyper-attached. Luckily, I also have two mini donks, and they each have one.
I also found that after I treated the one for ulcers, he got much better. When he starts being stupid and running the fenceline (even with his donkey), I add some ulcer meds for a day or two.
You’ve also got to get them on a frequent pattern of being separated. Ship him out frequently. Put him on the trailer all the time. Take him to the washrack and give him a bath without her. Go handwalking away from her. It might just be for a few minutes at a time, then gradually you can extend the amount of time you have him away from her.
This is not a situation you can just fix and forget about–you have to keep maintaining what you’ve established so that they can deal with going away and coming back and not having an utter meltdown.