The advice that Crusher gave you is exactly what I would recommend. You shouldn't have to "WIN" when referring to a relationship. It is not a game nor a competition. If a person wants to be with you...there should be no questions about it.
The unfinished business that she wants to finish shouldn't be an excuse for her to contact the online woman. If the online woman contacts her then she will just let her know where she stands then.
You may be the best thing that ever happened to her but like Crusher said is "SHE" the best for "YOU"? You may feel you love her but is she good for you? (True love) never dies so ask yourself if the love you once felt and then went away and came back..is it really love or something else?
I know it's hard trying to see through all of the smoke but take some time and soul search. Don't sell yourself short, you deserve the best for yourself. Not saying that she's not the best but she seem as if she's in a place emotionally that isn't where you are at this present time.
I don't know if you've be following the thread but we've been discussing "Balance" in relationships. Does your relationship reflect this?
Crusher did a great job in remembering the 5 love languages...just let me insert 4 and 5.
4. Words of affirmation = positive validations, uphold, uplift, confirm.
5. Acts of Service = doing things for your mate.
As Crusher explained. We all have a love language that makes us feel loved, as a result we usually feel this is what will make another feel loved and we proceed in doing those things. However, if the other persons love language is different then yours, you should find out what it is that makes the other feel loved and do that for them.
I hope this helps!