What's the situation re: his contact with them? Does he have time alone with them, does he see them away from you etc?
If they see him regularly alone, you need to keep it simple and say that you're going to court to make an agreement with their dad about when he gets to see them and where you're going to live. Don't say that it's a big stressful battle, just an agreement between two parents that love them. Tell them that it can be upsetting for adults to make this agreement, and sometimes it makes you angry at each other, but it doesn't mean anything bad will happen, and that you both still love them. Tell them that there will be a decision made and you'll tell them when you find out, and give them a rough idea of the possible outcomes.
If he's bad mouthing you, the very best thing you can do is be respectful about him. Tell your children that he's upset, and when people are upset they say things that aren't always kind. Tell them that he'll calm down soon and the agreement you're making will make things better. Keep talking about his good qualities as a dad (if he has any!) and talk about happier memories of him.
The last thing you want is for him to have ammo to accuse you of turning them against him- so kill him with kindness. Then if he does speak to them alone, they can tell him that all you ever say about him is nice things.
Don't overwhelm them with court details, just assure them that's it's friendly and civil and just a formality to make a plan together. If they ask questions, be honest. But try not to overload them with anything that'll make them overthink.
I really hope for the best outcome for you and your children, and I hope the NMO is granted and gets you some peace.