Hi ken ken,
Sounds like your gf is really really angry with you. I m not her and I do not know the content of the messages you have with other women. My hubby cheated with prostitutes so I m in no position to comment on her treatment towards you as my thinking would be unfair to her. Cheating is the most hurting thing a bf or spouse can do to their other halves. My hubby is worse than you so to me maybe your mistakes sounds mild as compared to my hubby. But even if my hubby didn't cheat physically, I too would be extremely furious and humiliated with my spouse's flirting with other women online or over phone messages too. Whichever form of cheating is still cheating yah. And the trust is definitely broken. Since she is not legally married to you, it sounds logical that after confirming your disloyalty, it would be more safe to not trust you and marry you. If I put myself in her situation, I would probably choose not to marry you too because the trust is broken and I wouldn't want to handle the messy divorce in future when you cheat the second time. Marriage is no bed of roses, it requires a lot of effort and commitment, why would someone trust you to be honest and loyal when you can cheat even before marriage?
I understand your love towards your Daughter but you have to ask yourself truthfully. You Want to Mary her because of your Daughter or because you really love her? You understand that it's Two different issues right? There are men who love their kids but they don't love their spouses, hence, they come home end of the day but they have gfs outside or they visit prostitutes outside instead of making effort in their relationship with their spouses. Then it's unfair to expect the Wife to remain as Wife while the hubby's hearts is somewhere else. Thinking along this line, I wouldn't want to marry you too if I were in her situation. And honestly, both you have sexual issues too. I don't know her real reason for rejecting intimacy, maybe it's the hormones after giving birth, maybe she's really physically very tired, maybe she has Low sex drive all along or maybe she doesn't really understand a man's need for intimacy. It might be temporary but it might be permanent. I think this needs to be communicated as well. If you think Pratically, if both of your sexual needs are not balanced and both you cannot come up with an agreed pattern where both are comfortable, then it's going to pose Long term problem as well. Then what's the point of getting married??
With regards to your Daughter. I think she is angry with you so she cut off your contact with your Daughter, which is understandable but of course, not reasonable, because you have the right to see your Daughter as Long as you didn't pose any harm to the baby. But being a gentleman and understanding man, I think you may need to give her more time to cool down before you can negotiate the right to see your Daughter. I would say that your focus is to gain her trust and willingness to talk to you so that you can have a clearer picture and even a proper closure etc.
Kudos to you for the emails and buying of baby stuffs to place outside the house. My suggestion is that you continue doing this. Maybe she would be touched and finally decide to communicate with you one day. I don't know the content of your email but I suggest you don't talk anything about marriage etc. I would suggest you let her know clearly that your constant effort is to have a chance to have proper communication with her and a chance to see your own Daughter. No pressurising issues about marriage or intimacy.