How do you find out for sure if your husband has fathered other children outside of your marriage?

There has to be a lack of communication in your relationship. The only way you are going to find out is by asking him. Talk to him calmly and ask him and be sure he knows that you will understand if he admits to it. However, if he should have a child and is not supporting that child then he's a slacker and I'd ditch him.