I think OP is fine. Maybe overreacted a bit thinking she needs to leave, because nothing indicates the BO permits this or knew anything about it.
Your average boarder doesn’t want to know what goes on “behind the scenes” on a farm. Same as BOs, like me, who “take care of” problems like raccoons and opossums. Yes, it needs done and everyone sort of understands that, but I don’t do it in front of the boarders! They don’t want to think about it, hear it, or see the results. It is quietly taken care of during off hours.
Same as when we have to euthanize a horse…I close the barn until it is buried or removed. No one complains. Lesson kids and boarders don’t need see dead horses.
I would expect the BO to instruct the workers not to dispose of their goats on property because it upsets the clientele (or do it after hours and make sure all evidence is well out of sight, no live goats are there to make noise, etc., if there is no other place and they live on site.
In our family farm when we kill deer they are on property, but hung in a private building where no boarder has any business being. Meat does usually need to hang for several days after slaughter, but they could put up a tarp or lock the shed or whatever. Surely accommodations can be made to satisfy both parties here.