If you have a criminal record, be honest with your children about it. Tell them what you did and why, be brave enough to accept their response, and never deny it. If nothing else you can use that experience to keep your children from repeating your mistakes.
They will find out eventually. It is better that they find out from you.
Rocmike's alias Dr. Kelly is starting off today's posting marathon. 3 hours of posting so far. With some anonymous posts sprinkled in.