Dealing with a 10 year old daughter I just found out about?

I think you should get joint custody of her, period. Fight for it and keep it enforced! Then do just as you are and be consistent with her. How you treat her, how you love her, etc. Maybe you could talk to her and tell her how much she means to you and how happy you are to have found out about her. Tell her how you admire her and care about her. You or your wife should also tell her that if she has ANY problems and needs someone to talk to, to call anytime of any day and you'll be there as fast as you can. This must be hard for you, but for her must be crazy hard. You're doing everything you can!