DO NOT warn her about exposure... YOU expose FIRST ... THEN you conront her...
If you WARN her you are going to let everyone know she will run damage control behind your back and discredit you before you can bat an eye
Expose to everyone else first... THEN when she confronts yOU becuase word has gotten back to her you hit her with the above...
I would put more in there on the harm that she's bringing to her children... Its a biggie... mention their names if you can
Don't tell her "find other living arranagemetns"
Tell her "your affair is not welcome in this home, our children need an honest, commited, loving enviornment, not the torture chamber you are bringing into our house - leave"
