The key here is to make this a do-or-die conversation. Tell the customer the truth, and then tell them you’re not going to work for them any more if they keep the other morons on the payroll — you’re not going to risk your reputation and your business on being associated with that other company.

“I’m sorry if this means we can’t do business any more, but this situation has gotten so severe, that I just have to tell you the unvarnished truth, and ….”