First off, you shouldn't let what that woman said bother you or get you down. Secondly, I feel your husband kept this a secret from you thinking that if he told you, your opinion of him would change. Every man has skeletons in their closet, some are reluctant to reveal those skeletons because they don't want the one's they love to think any different of them, they don't want to be judged for past actions. Of course i'm not justifying what he did but you should give him the benefit of the doubt.
As for the paternity issue, you did the right thing telling her no more child support will be given until a paternity test is taken. Stand firm with that decision don't sway and don't let him sway either. If this issue comes to the point where you are standing in court, you can request a paternity test, then she will have to take one. However, if he is the father, and court order claims him to support the child, there is nothing you can do.
Don't call this woman anymore, if there is something to be discussed send her a letter requesting her signature, the post office will require a signtaure from the recipient allowing you to prove that you sent a letter and she received it. Keep copies of everything from receipts to letters. Don't ever pay in cash, pay in check so you have proof you paid.
As for your husband, as stated earlier, he just didn't want your image of him to shatter, although it already has because of him trying o hide this from you. One of the most important things in a relationship is communication, he hasn't been communicating with you and subconciously you know this, and it angers you. Try doing your own counseling, tell him how you feel, don't hold anything back, listen to what he has to say and reflect on it. Ask him why he hid it from you but not in an angry tone. Try to do calming, binding activities together to ease the mind. Just communnicate, trust and love each other and you will pull through this. Nothing can stand in your way, you can do it :)
Good luck hon.