There are probably others here with more experience on how to handle the kids. My only advice to you in their regard would be to always tell them the truth, in an age-appropriate manner.
If you wife brings up D or LS, then say "I don't want a divorce. I would still like to work on our marriage, and hope you'll end your affair and work on it with me." When she asks you again, say "I haven't decided anything new; my position hasn't changed. I do not want a divorce." If SHE says something like "I can't live like this!" or even "I want a divorce!" calmly say "I can't stop you from doing what you want to do. I don't want a divorce."
