Generally, if you have petitioned for divorce on the grounds on one year's separation (desertion), you must prove you have had no contact or support for one year or more. From what you have written, it seems that is the case, although you mention nothing about support.
The standard the court will use in determining what will happen with the children is 'best interests' of the children. Assuming they live with you and/or the father, and the situation is one that is in the best interests of the children, the court will in all likelihood keep the situation as it is.
I seriously doubt the judge will take you to task for having two children while still technically married, because, unless there is something you have not revealed here, it has nothing to do with this case. I also seriously doubt that any judge would call you names, particularly in open court.
If you still are not reasonably comfortable with the situation and have questions, I strongly suggest you consult with an attorney experienced in family law. This website has contact information for attorneys in your area and I'm sure one of them will be glad to consult with you.