This would be at the top of my list, too. Besides an ulcer regimen, I would also have the mare’s eyesight checked, just in case.
Since the mare was already upset about being in a new environment, the pig may have been the tipping point. With my old horse it wasn’t pigs or goats. It was chickens, geese and one particular emu. He could not deal with large feathered things. Ever.
I’m also wondering if this is a mare who has always been the passive, subservient one in the herd. So she lacks confidence and the world is a scary place unless she’s protected by her more dominant herd mates. It can be tough to connect with a horse like this because they’re uncertain of everything. It takes a long time of being firm yet fair. Require her to be respectful and behave yet reward good choices. Maintain a consistent daily routine. In essence you are becoming her Boss Mare and teaching her that the world is okay, after all. (Except for maybe the pig).