I don't find the expectation that one not fall in love - especially with partner which whom they are regularly seeing - realistic. Humans can control behavior, but not emotions. For example, when I walk into restaurant and smell (insert whatever your favorite food is here), I want it. It doesn't matter if it is not good for me - too many empty calories - I still desire it. I can choose not to order it - control my behavior - but I have little choice in the wanting.
Love is much the same way. Your wife could choose not act on her feelings, but she cannot prevent their existence.
Asking her to end it with the other man, doesn't erase the love that already exists. You can pretend that it does, but it does not.