It sounds like there could be several reasons for her behavior.
The first step is to see if she is willing to see a doctor for a thorough checkup. Although it is very early for Alzheimer's, becoming combative and angry is one of the first signs. It is highly unlikely this is what your wife has, but it would be neglectful not to mention it as a possibility.
Your wife should also be screened for hormonal problems. Her endocrine system could be affected and there could be a number of disorders that can occur to cause her behavior.
With your wife being told by more than one person in the family that you were cheating was probably too much for her. If trust was shaking in your relationship before, she might have felt there was little choice but to believe it. Her acting out towards your children and others could be the misery she feels about your marriage. However, it does sound like from your description that she has some unresolved problems from her past that would make her susceptible to angry behavior. If so, she could be unable to separate her unresolved anger issues from the lies she was told about your behavior.
If you have not already, ask her what it would take to allow her to trust you again. There must be something that would prove to her once and for all that you can be trusted. If she is unable to come up with something, then this problem is about her own personal issues and not the trust issues in your marriage.
Since she will not go to therapy with you, she gives you little choice. Does she know about your desire to divorce? I ask because it could motivate her to go to counseling with you. Also, if you attend church you could see if she is willing to talk with your pastor with you. Sometimes therapy scares people but talking to a pastor is easier because of the nature of faith and church.
You may also want to consider a separation instead of an outright divorce. It is hard to know what will affect your wife, but seeing that you are considering divorce may shake her up enough to be willing to work on the issues.
Here are some resources that may help you as well:
Should I Stay Or Go? : How Controlled Separation (CS) Can Save Your Marriage by Lee Raffel
Healing Your Marriage When Trust Is Broken: Finding Forgiveness and Restoration by Cindy Beall
When Love Stumbles: How to Rediscover Love, Trust, and Fulfillment in Your Relationship by Randi Gunther
You can find these on Amazon.com or your local library may have them for you.
Present some of these options to your wife and see if she is willing to work on the issues with you. She is leaving you very few choices in this situation so hopefully, with more options to consider, she will be able to move beyond her anger and begin healing.
I hope this helps you,