I don't know if it's "appropriate" from an "I don't own my partners" perspective... but I, personally, would be playing the "If you really love me and value our marriage, you would not ask about going through with this" card.
It's one thing to cheat, and then get caught and keep on cheating for almost a year. It's one more thing to then try and turn that cheating relationship into a poly relationship. But it's another thing entirely to allow that cheating partner to try and break up your marriage. And make no mistake, she had that ability only because he gave it to her. He and he alone had the power to say: "You are not respecting my marriage. Our relationship is over." But then to turn around two years later and do it all over again? Please.
She is what she is. She does not respect boundaries and she's fixated on stealing your husband. I won't waste time talking about her changing, because that won't happen. But your husband need to get his act together and realize that he's asking to bring a toxic person into your marriage.
That being said, I probably wouldn't say "I forbid you to see her" because:
1. You don't own him and you're not his guardian. You're not allowed to tell him what he can and cannot do.
2. He'll probably lie and do it behind your back.
I would, instead, focus on trying to get him to see her for what she is and see the potential harm she may bring to your relationship. Then ask him to make an informed and educated decision, specifying that you'd prefer he tell you if he's going to see her anyway, rather than cheating again.
See if you can get his other girlfriend on board, too. This ex will probably be as harmful to their relationship, and it's really difficult for men to win any argument against two headstrong women!
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker