I think when they talk about secrecy, they mean do her parents know? Do your friends know...and the big one, does the OM's wife know? Is OM married? Sometimes outing the OP is all it takes to end this stuff.
BTW with consequences you want to try to avoid making it a tit for tat situation. If you do this I'm going to do that. You want it to be where she sees that if she chooses a certain path she will bring x and y upon herself. The difference is subtle. I am not explaining it very well but it seems this is a part of your game plan that needs improving,sheesh, newbies ;-) Hopefully someone will come along lower down and explain it better.
I think you described it VERY well, DownNotOut. This is precisely what you want to convey.
From my own archives:
The best way I can answer that is that if you make it about HER, they will come across as "demands" and being "controlling."
If you make them about YOU, and what YOU need, then they are "boundaries of personal integrity."
Example:
"I forbid you to see OM" = CONTROLLING
"I can't live in an open marriage" = BOUNDARY
"You need to check in with me every day, and give me your cellphone bill!" = CONTROLLING
"In order to feel safe in our reconciliation, considering your recent affair, I need to know that you're no longer talking or texting him by having the cellphone bill come to me for awhile" = BOUNDARY
"You can't talk to me that way!" = CONTROLLING
"I like ME too much to allow myself to be spoken to so disrespectfully. Please come back when you've calmed down, and we can talk further." = BOUNDARY
Make sense?
It's also HOW you say it. It should come across as something you HATE to have to even ASK for, and that you'll COMPLETELY UNDERSTAND if she doesn't feel she can do it, but hey -- this is what I need right now. Let me know."