Congratulations on receiving your NL..
First off, are you legally married with a registered marriage certificate?
If the answer to this is yes, then you have a problem. When you fill out the forms (DS230 etc) to return to KCC, you will have to state your marital status, your wife's name and DOB and your kids' names and DOBs and remember also that in your interview you will have to swear before the consular officer that every information on that form is the truth.
Scenario 1: you leave off your wife and kids' info and go for the interview and swear that you have no wife and kids. You may get the visa but 5 years in the future you will want to file for them to join you, what will happen when they realize that you were lying on your initial application?
Scenario 2: you fill out the forms truthfully including your wife and children in your application. Chances are very high that you will be disqualified because you have now included persons in your case who were present but not included in your initial DV entry.
Scenario 3: You are not legally married so you have no wife in the true sense of the word, OK... but you have the children and you did not include them in your DV entry. According to the rules you should be disqualified for not including your children.
I make no assumptions about your case, just wanted to lay out the facts as I understand them so you can make a decision for yourself.
Good Luck my friend...