One Question: Do you love the mother of your child? If yes, drop all contact with the 19 year old girl, and come squeaky clean with your (ex)Fiance. You can't play this "only friends" game with flings. The only way to bring back trust and consequently your girl is to do whatever it takes for her to be comfortable again. This can include following unreasonable expectations, illogical new rules and the like.
IF you truly love her and want to stay together now, you have to abandon yourself and throw yourself at her mercy and pray that she will have you back. It could all backfire, but that is the only way to even attempt to patch things up.
Now imho, you should have come clean back then. Or even better not cheated. I can't say that I feel sorry for you, or anyone in your situation. I can say this: think how terrible your girl and daughter feels now. What can you do to make it up to them?
(PS. the after throwing yourself at her mercy and doing anything unreasonable that makes her feel better, she should drop this. If she holds it over your head, she is on a power trip. Go to counseling.)
edit: Sorry if I sound like a uncaring person, but tough love is the only way to get to some ppl. Best of luck to you, your ex-fiance, and daughter.