I agree with @MimiSunshine Children can take the truth. I would tell them (in an age appropriate way what has happened) and it is also ok to say mummy is is hurting right now and this is why it's hard for you to hear the OW name (after all, anger, sadness etc are normal emotions that we need to teach children to navigate, and also teaches them that they can overcome those feelings and they are not a mystery) but you are not angry or upset with them, and you want them to enjoy themselves when they see daddy, because ultimately when they're happy, you are happy. And they should not feel guilty.And in time it will no longer hurt you so much to hear OW name, but for now it hurts.
I personally do not subscribe to not allowing children to be upset with the parent that left (after cheating) and bending over backwards to present them positively. Whilst you don't want to totally ratbag them, there is zero reason to prevent them from knowing what Dad did was wrong. Children have a right to expectations regarding their parents and he has let them down. It's ok for them to know the truth and ok and actually important and healthy for them express their feelings and be upset with Dad for a bit. Its also vital for them to understand the link between behaviour like cheating and consequences. Obviously you don't want to egg it on and you want to be age appropriate. I would tell them daddy's not making very wise decisions right now, but he loves you no matter what (I mean I have issues with even this narrative but that's another thread entirely).
All this 'everything is fine, all is good, no the OW is lovely, smile, smile, happy, happy, hide tears, mummy is made of cast iron, daddy is just making a different decision, one decision is as good as the next, is teaching children that there are no emotional consequences to bad behaviour. They matter. Daddy hurt them too (I am not suggesting you say that) You matter. You can be sad in front of them within reason. As you come out the other end they will be inspired by you.
I went through it. But my kids were much older so it didn't apply in quite the same way but as I also have boys, I let them know their fathers behaviour was not something to trivialise or brush over or ever emulate in the future because of the utter devastation it causes. They are well adjusted and they are bemused by their father's decisions now and they know they can trust me to always tell them the truth.