The two sisters stopped and were unified on the fact that Webber reminded them of their deceased mother.
Finally Dr. Webber (who had been caring for the women’s sister) got in the middle and finally set Alyssa Milano and Holly Marie Combs’ Haylee and Heidi straight.
The fighting continued throughout the episode, and was becoming a disturbance to all the doctors on staff.
Regardless of whether or not their sister could hear them, this fighting was helping nothing, and aggravating everyone.