You should probably have a conversation with your W about what you will both tell the kids. I don;t think the kids need to know the details other than to know you and your W are having some issues you are trying to work through, that you both love them very much and that no matter what, you will always be there for them.
It's ok to acknowledge you miss them too. Then spend as much time as you can with them - and don't worry about what your W thinks about that. They are your kids too, and they need both of you.
