I too dreaded that convo of telling my kids. Granted my WW moved out before we did, so I think they knew something was going on....I did some research on the bullet points to cover, discussed it with my WW and told her that she was the one that needed to deliver the message. It wasn't as hard as I thought it was going to be, they probably already know something is wrong and the reassurance that mom and dad will always love them might help. We didn't say the D word, just that she needed her own place. I think baby steps is best, but I have seen it both ways. I actually felt a huge weight lifted off me once we told them.
Only thing was WW told them she just needed her own place for a "little while" so I think they still hold onto her coming home. Do the research and let her deliver the message and your job is to NOT CRY, or BE SAD. You need to act positive for them, and just shower them with your love, affirmation, validation. Also, do it somewhere you can all get dessert or something right after to change the subject. No easy way, but know it will not be as big of a deal as you think