It's great you got to spend some time with your (potential) daughter! I can't imagine how nerve wrecking the wait is...
A few more weeks and you'll know for sure. And from everything you told us so far, I find it highly unlikely that you'll be able to reliably settle this with her without an official third party. This is also going to be a huge and emotionally-charged change for her. Mothers tend to be (at least in my experience) quite possessive of their newborns or small babies even when they are on good terms with the father (I know I had a hard time trusting DP with DD in the beginning and it took a lot of holding back on my part to not interfere in his relationship with her). So imagine she has to give up control to someone who is practically a stranger (to her). Most like there is going to be a lot of resistance on her part. While understandable, it's not fair to you.
Best of luck!
I'm trying to stay rational and keep all of this in mind, but it's really difficult sometimes. When she first told me she was pregnant as I was upset I was told, "well just imagine how she feels! She has to carry the baby." And then when she started ignoring me during her pregnancy I was told, "well just imagine how she feels! She's pregnant so her hormones and emotions are all mixed up" and then when she had the baby and continued pretending I didn't exist I was told, "well just imagine how she feels! She just gave birth to a child. There's so much going on for her right now!" And now it's still a matter of "imagine how she feels! Mothers are very protective of their newborns. she isn't going to easily let you have access."
In my eyes, she's been showered with gifts, congratulations, warm smiles, a new boyfriend and apparently a house, and most importantly a beautiful baby girl for her efforts. And I've had the pleasure of being called white trash among other things by family members, commonly being told I was "trapped" and my life is "ruined" by friends, losing every shred of desire I once had to date women, trudging through the awful family court system, and dealing with her manipulation and immaturity just for a brief glimpse of my daughter at Applebee's.
I assume most of you posting on here are women, and many of you have experienced pregnancy and childbirth. I haven't. I didn't even see the mom once when she was "showing". As much as I feel like I should have some sort of bond with this baby, I certainly don't. I'm a complete stranger to her and she is to me as well. So really, I'm hanging all of this on a prayer that it is the right thing for me and more importantly for this little girl. But right now I don't know anything beyond that prayer, and it plagues me most days.