It is very hard to trust when you are not even sure of what happened. And if he is not telling the truth, then he is not taking this seriously.
An affair of any type is breaking the marriage vows. Affairs undermine the trust of a relationship and without trust, your relationship falls apart. If your husband is not willing to tell the truth even now, then he is not serious about repairing the marriage. This is also evident by him destroying all the evidence. He is showing that he is worried about himself and the fact that he hid the truth in the situation.
The only way the marriage can ever work is if your husband is completely open and honest about the affair. He also must tell you what you want to know. And he must be available to you whenever you need reassurance that he is where he says he is.
He must also be motivated to regain your trust. He can do this through working towards repairing the damage he has done. The first step is ending all contact with this other woman. That means all texts, emails, phone calls or other contact. He must be willing to show you his phone and allow you access to his computer and messages.
The next step is to see a counselor. The counselor can help mediate how to repair your relationship. They can guide you and offer insights and suggestions on how to handle the bumpy road back to trust. To find a therapist, ask your doctor for a referral. If you attend church, your pastor may be able to help. Or you can search on line at http://therapists.psychologytoday.com/rms/.
Another step is for your husband to find out why he had this affair in the first place. It is common for the cheating spouse to try to blame the affair on the marriage or other spouse. But problems in a marriage are not solved by affairs. Affairs happen because the problem was mishandled by the cheating spouse and instead of facing it and resolving it, they took a self centered approach and cheated. So resolving the reason behind your husband's behavior will help prevent the behavior in the future.
You can also work on this at home. Here are some resources to help you:
Infidelity: A Survival Guide by Don-David Lusterman
Not "Just Friends": Rebuilding Trust and Recovering Your Sanity After Infidelity by Shirley P. Glass and Jean Coppock Staeheli
Surviving Infidelity: Making Decisions, Recovering from the Pain by Rona B. Subotnik and Gloria Harris
You can find these books on Amazon.com or your local library may have them for you.
Take your time and see if your marriage can be repaired. Since there are children involved, it is worth the effort to try. If your husband does not participate, it may mean the end of the marriage. But if he is willing, then it is very possible for your marriage to survive.
I hope this has helped you,