So the one thing that pops out at me is the entire OM/Kids thing. Been there done that .... here is the deal with all this. in your MLCr YOU are the roadblock between her and the euphoric happiness she is hell bent on achieving, with this in mind you bringing up how you forbid any contact of OM with your kids will simply come across as controlling and you trying to stamp out her happiness. She will most likely monster as you predict ... or maybe she wont ... we can never predict how a MLCr reacts but what I can tell you is you can not control what she does, who she does it with, where she does it, what time ... you catch my drift here? Its out of YOUR control so the only thing you achieve by saying "I am not comfortable with the kids being around OM" is showing your emotions/feelings ..... this will just be more ammo for her to put into her justification shotgun that she has been loading during her crisis.
She most likely knows you do not want OM around the kids without you saying a word ... so don't. Sure it stinks ... My W had OM and his kids over making Ginger-Bread houses like a new little family, stung like a bugger but there was nothing I could do about it. Me making a scene was not going to do a darn thing really.
One thing that is hard with this .. move the focus from her and what she is doing toward you and what you CAN be doing ... that's the only part you truly control, its the only part where you can get better and grow in all this ... she is on her own path and you are wasting time wanting to point out the potholes on her path ... pave your own road.