First off, her reasons for her behavior do not sound like they come from someone that is contrite. Rather they seem to blame other outside causes, rather than a character issue with herself.
You ask for opinions, and if you have read anything I have written here, you will probably be surprised with this one.
I would suggest that you seek sole custody of your children. You may find that your wife is more agreeable to this than you might think. Then I think you should divorce. The best time to do all this is when she is feeling remorseful for her actions.
If you decide to continue on, you are very likely to experience the same pain you have already been through, time and time again.
The reason for sole custody is to spare your children the pain of a long string of new 'people' in their lives. If they stay with their mother, this is the likely outcome. Also, the potential for child abuse is greater with increased exposure to people with unknown histories.
I am sorry that I could not offer more encouraging advice.
All the best, -NOPkins-
I will ferret out an affair at any opportunity.
-An affair is the embodiment of entitlement, fueled by resentment and lack of respect. -An infidel will remain unreachable so long as their sense of entitlement exceeds their ability to reason.