You have every right to expect honesty out of the women you have chosen to spend your life with. And if she can not give that to you eventually you will begin to resent her which is never a good thing.
It is good that you have the heart to forgive her, just keep your eyes open and your intentions clear going forward. The biggest problem is trust of course, you feel she is hiding something and she feels you do not trust her. While love may be enough to keep people together it is trust that builds a relationship up and keeps it strong.
You are going to have to have a sit down with her. Basically find someone to keep the kids over night and let her know that this is the time to talk. Ask her to please listen to you without speaking so you can say what you need to say. Let her know how you feel about her and about what has happened. Explain to her that you want to move forward and leave what has happened in the past. But in order for that to happen you must first be honest with each other about everything and spend the evening working on why it happened and how to prevent it in the future. If you already know you plan on forgoing her then let her know. Explain to her that while you plan to forgive her regardless of what she has done........she must give you her trust and tell you the truth. Explain to her that as long as you feel she is lying to you that you can not trust her and this is a very big issue for you. Let her know that regardless of what she has done you need to know the truth so you can move on.
Now comes the trusting part............because this is about more then just her. If she tells you nothing happened, then you must trust her. I know it will not be easy, and at the end of the day it will be hard to believe. But the fact is you must trust her........if at a later date you find out the truth then you have a reason to be angry, but at this point unless you can prove it or she fesses up you may never know. Holding onto that distrust is going to hinder your relationship far more then anything else.
In the end we will hope that she will be honest about what she has done, try to remain calm and get the information you need. Talk about what happened and why it happened. If she says she does not want to go over the details explain to her that you need to. Let her know that since you are being strong enough to forgive her she must be strong enough to tell you everything so you both can work on it. Spend the evening on the subject and get what ever needs to be out into the open. If you have made mistakes then this is the time to be honest as well. Not only will it remove any stress you have about it it will also show her that you are serious.
In the meantime I would also not talking about it until you sit down with her. Let it go for now.......otherwise she is going to continue to feel like she is under pressure. As for the "crazy mother" I would suggest explaining to her that you are working on it and in the future unless she has some proof you do not want to discuss it. This prevents wild story's and covers you in case there is something going on.
Since you have children this needs to be dealt with, the fact is the kids deserve both mom and dad to be able to communicate when there is a problem and deal with those issues without it causing harm to the family unit itself. Your children are young.....but they can sense the stress going on between you and mom and the last thing you need is for them to become hurt by all of this.
The sad reality is infidelity is a hard thing to get over, I would suggest that you set up a marriage counseling session as well. These are very helpful to every marriage. The counselor is not going to pick sides or even tell you what to do. The counselor will help you both learn to communicate better and learn to trust each other.