Well, she's been lying about something, and she's feeling guilty about it.
You have two options before you...
1. "I know you've been seeing someone. Maybe even more than someone. There are simply too many inconsistencies in much of what you've been telling me. I want the truth, and I want it now."
If she wavers at all, stay on point -- you want the truth, and you want it now. At the same time, don't go into details regarding the inconsistencies. Make no mention of what doesn't add up. This will give her no opportunity to gaslight.
The problem w/ this approach is that, if she is cheating, she'll likely just lie about it.
That said, you know your wife. If you think you can get her to crack w/ a stone-faced semi-bluff, go for it. If it doesn't work though, and there is something going on, she'll just take it underground, making it even more difficult for you to detect.
This isn't the specific approach that I extol, but it can meet some degree of success. One can make your option #1 more successful by objectively scrutinizing her response. The problem with confrontations is that individuals tend to be asking for the truth, rather than laying it out. If one is asking, then it is implied that there is room for an argument/debate.
There are other behaviors that need to be seriously addressed, as well. Fits of rage have no place in a healthy relationship. I say this to highlight the need for there to be serious consideration given by her. She can't just give a believable excuse and all is well.