A good game of, "Let's you and him fight".
Nailed it. It looks like Bahwa would like to fire LoudMouth, but couldn't figure out a way to do it until The Donald stepped up to take the fall by goading LoudMouth until she broke and cussed out Bahwa to her face, in front of one of the studio execs. Never underestimate the power to manipulate events by an old, hard broad.