OH GIRL.....have we ever had this problem!
As chapter president I went to the "other organizations" president and I went to one of the drum majors who also was in that sorority. I told them my concerns and flat out said, "if you want a war, we can bring you one. But I highly I doubt you want that...." they didn't and I think they were shocked I confronted them about it. So now we are growing and trying to get along. I and the XYZ's sorority president sat down our chapters and flat out said - no more bad mouthing, or YOU will be in trouble. Because I guarentee it, no matter how hard you think your girls aren't saying anything back, I bet maybe one or two are or have.
If this doesn't work, the way it goes at my school is all chapters have a sponser that is one of the teachers in the fine arts department. Flat out go to them and say, ma'am/sir our organization is having difficulties and we dont' know what to do. It may seem like tattle telling, but if this is your third resort its worth it.
PM me if you have any questions, I'm sure we discuss this better in a private matter