The golden rule in this situation is not to lie.
Ideally, agreeing beforehand what will be said and telling children the news together is best but even then, some honesty is required. Couples often soften this by saying things like: 'Dad has/had another girlfriend and that's not really allowed when you're married' and 'the trust has gone and when it's about something like this, a marriage can't go on' while emphasising all the time that this is something that's happened between the adults and is no reflection of their love for them.
It's also important to answer follow-up questions with some honesty about the feelings associated with the break-up and what led up to it. Admitting to hurt, sadness and even anger is okay because this gives children permission to feel those things too, but there needs to be some accompanying guidance about how to channel those emotions appropriately. So it's okay to say "Yes I am/was angry and sad about it, but I'm talking to a counsellor/friend/my mum about that and hopefully Dad and I can be happy in the future even though we're apart and those feelings will fade" This demonstrates to children that strong emotions are normal, talking about them is helpful and that there is some positivity about the future.
Children are most of all concerned with how the situation will affect them personally - where they'll live, how often will they see the NRP, whether they'll have a second home etc.
In a case like this where it is anticipated that a partner will lie to his children, or threaten to do so, it is even more important that the OP tells no lies herself. But it's possible (and preferable) to tell the truth without demonising and vilifying the other partner.
It's a good thing for children to learn that some behaviours in marriage are intolerable and that forgiveness and new trust are only appropriate if someone has confidence that the same thing could not happen again.