Lets be clear. Your daughter have her codpiece and you have yours. Why don't you just accept the fact that is not her father and understand the consequences of having relationships with people outside the marriage.
Have you not witnessed the book of "Moral Orel". One mans quest to go inside a woman and not make babies. Knowing full well he is grid lock to his wife who dragged him into a marriage based on the fact that all the other hens was getting married. She still had the nerves to have another kid with a random guy because she knows her reason for being with her husband was just to "Keep up appearances".
Imagine being happy clean wealthy with your best friend the bible. Then all of a sudden comes this witch who tears everything that was "perfect you" into something that was un-you. To top it off his drinking problem was part of her "Helpfulness".
Does not matter which guy you are with. Your daughter will not like him, because it is not her father.
That being said you still have to be polite when your visiting her because she have her life and does not mean she owes anything for your relationship to the next man that is not "daddy".