"What? What? Can you hear me? We have a bad con. . . ." <click>
Sorry, I couldn't resist.
You're right OP, it doesn't sound bad. It sounds horrible!
My suggestions involve a mindset change on your part. On your part because until your leadership decides she's a liability and gets rid of her, you're subject to her behaviors. Unlikely you can change her, only your response to her. Put your nursing hat on here and ask what the motivation for changing her behavior would be. What can you appeal to?
You can't do anything about her being disruptive and creating chaos. You can only decide that her judgments and orders don't concern you, they're just the rantings of a deranged pitch woman.
Following is some language you might find useful. None of it's designed to change her or change her mind, just designed to create boundaries between you. I'm not sure I'd work too hard on learning to speak her language. The problem here isn't, as they say, a "failure to communicate", it's her bullying and lies and other unethical tactics. So I wouldn't spend much time trying to educate her about how it needs to work. It sounds like she just gives you lip service and goes on the next target, so its a waste of your time to try to explain.
"Thanks for your input, I'll keep it in mind. I really need to get back to patient care now."
"That makes total sense from a marketing perspective. Unfortunately, I need to follow good nursing practice so as case manager I'll be implementing _______."
"You and I see this differently. I need to refer you to (insert boss') name here."
"We remember this differently. What I'm going to do going forward is. . . "
"Speaking just for myself, I need to practice within the Conditions of Participation. So as soon as I am provided with ____ , I can do _____ ."
"I feel the urgency of your request, however right now my priority must be ____"
"What I can do here is ______ . Regrettably _________ isn't an option."
There's nothing you can do about her lying to you or about you. Your leadership knows about it and is banking that she can bring in enough dollars to justify the harm she's doing to your agency and its reputation as well as staff, patients and families. There's nothing you can do about her screaming at IDG, or bullying your colleagues. But you may be able to carve a tiny island of sanity out for yourself in the middle of this mess.
Good luck, you make me really glad I don't need to contend with one like her!