Exercise to get younger and older worker working well together?

I am new to a position where I am managing a small organization with only four other employees. Two of the employees have been “working” together for a few months but haven’t been getting along well. They haven’t had anyone around in a leadership position (the home office is far away) and these two have been building resentment toward each other. One is a young, 25 yr old Puerto Rican from the inner city and the other is a 55 year old white woman from the East Coast. The older worker is much more experienced than the younger but the younger was told that the older one was to be the office “administrative assistance” which she took as her license to be bossy and condescending to the older worker. The older worker found this intolerable from the start but was unable to get anyone from the home office to help resolve. Meantime the older worker, because she needed the job, did her best to follow the orders of the other worker. The younger worker is an attractive, somewhat narcissistic, type with little insight into her relative lack of experience. Bottom line, the younger worker has been barking orders at the older one for awhile and it boiled over a couple days into my new job. I sat them both down and said we’d try to work together to mend fences but that they both needed to dig deep and think hard about how they could meet the other more than halfway—because if we’re not able to resolve the issues one of them would have to go within a couple weeks.

I’d like to offer more than just threats and opportunities to sit and talk about communicating and feelings. Is there some kind of HR exercise that’s especially effective at getting two people from different backgrounds and that have had some ill feelings about working with each other, start to collaborate more effectively?