Welcome to our forum.
I was also somewhat confused by some of your story, such as how each rule was broken by your husband's new girlfriend. Can she change, and start keeping the rules? Do you believe she can? If you're never able to trust her, then it will always cause a problem for your husband to continue in a relationship with her. How does he feel about the rule-breaking?
Is this perhaps not just a trust issue with the girlfriend, but with your husband also? Has he kept all the rules? Will he in the future? If he was involved with this girlfriend, wasn't he breaking the rules with her? Can he change and keep the rules in the future? Can you trust him?
Some kind of in-depth discussions are probably needed, at least with you and your husband present, possibly with his girlfriend (and her partner?) present also. If rules have been broken, then it must be made plain what you need to restore any trust that was lost.
I hope Polyamory.com is of some help to you.
Love means never having to say, "Put down that meat cleaver!"