I feel bad for you, but even more for the children. They should not witness your arguments, it doesn't matter if you are calm, this is adult talk and should happen away from them, if at all. If she places herself near them, you need to stop the argument.
Why do you feel powerless to stop the discussion or take control of this kind of situation?
I don't know your whole story but wonder why she is cheating but you have moved out?
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17
They should not witness your arguments, it doesn't matter if you are calm, this is adult talk and should happen away from them, if at all. If she places herself near them, you need to stop the argument. 
