I’m annoyed with myself for letting this happen
STOP. Just stop that thinking. It is unhealthy and will only make you feel more confused, and take on responsibility that is not yours.
Your partner decided to cheat, she made a mental decision to allow this person into her life, and then she made decisions daily, and even hourly to disregard her vows and promises to you. NOTHING you did or did not do led to that. DO NOT try to own this. It is not your fault, she didn't do this because of anything you did, or did not do. She did this because she is a broken person. PERIOD.
NOW - Focus on you, and your children.
Along with seeing an attorney, and a therapist, it is also a really good idea to see your Dr and get full STD testing. Yes this is necessary. You can ask for a referral for a therapist when you are there and if you are struggling with self harm, or sleeping and eating you can discuss that as well.
For most of us this is a big big trauma, and often people benefit from the help of medications to allow them to at least sleep and eat a bit. Without some solid sleep, and nutrition you will find it nearly impossible to keep your emotions in check, and your brain making rational decisions.
Keep reading, and keep posting. Know that while your situation is unique, that cheaters follow the same play book. It is as predictable as an afternoon rain in the summer in Florida.