Benwyck,
I hate to be the stick in the mud but...
I really want to urge you to be cautious with how you proceed with this relationship. Yes, she's biologically your daughter and I'm sure it's a relief and joy to her that you have not only acknowledged her but welcomed her into the family.
But that doesn't change the fact that she's a stranger. You've only talked to her a few times. You haven't met her in person, interacted with her, or seen her interact with others. You don't know what kind of baggage she will bring and how she will get along with and integrate into the rest of the family. While you might've been thrilled when she called you "Dad," the fact that she said this to a man that she has only just learned about and only spoke to a few times over the phone is alarming. It's akin to meeting someone online and proposing marriage before you've even had a first date.
Also, I can really understand why your wife feels like she's being pushed out of her own family. This is happening so, so fast. She never asked for another daughter or to take on the responsibility of being a personal mentor to this woman, yet she feels like she is being pushed to do so because her husband, children, and mother-in-law are ecstatic about this new addition. She probably thinks that you should be moving more slowly and carefully, but how can she feel comfortable voicing her concerns when she's likely afraid that she will be perceived as jealous, territorial, or unwelcoming?
My suggestion to is that before you start family counseling sessions and start reconfiguring your family to fit your daughter in it, get to know her first. Keep talking to her on the phone. Meet up with her coffee. And though I know you might balk at this, you might also want to run a background check, too, just in case there is anything alarming in her personal history that you need to be aware of before you welcome her into your home.
You might think I'm being paranoid, but don't let your feelings of joy and obligation toward this woman override your existing responsibilities toward your wife and other children.
[This message edited by BluerThanBlue at 1:47 PM, Friday, April 26th]
BW, 40s
Divorced WH in 2015; now happily remarried
I edit my comments a lot for spelling, grammar, typos, etc.