This situation does seem complex with matters that have changed since the original agreement. Any life situation that involves complexity and shades of gray warrant careful consideration, so I applaud you for doing so. Change is not easy, and it occurs in ways that are unpredictable.
Was anything established legally when this person was conceived? Are you named as a party in the action of serving as a donor to make possible the conception of this person?
Your question and description of the situation make me wonder about your intentions for establishing yourself as a biological parent. I also wonder if this has been on your mind currently in light of the father's alcohol problems or if you have contemplated this for years.
Seems like the bottom line may be what impact such revelation of biological contribution to this person's life is of primary concern. Is such knowledge likely to enhance her life or be felt as intrusive by her? I ask that with awareness that sometimes intrusive acts can lead to positive outcomes.
So, I wonder what the exact outcome is you hope for? Are you trying to move a particular outcome forward? In your question, it seems as if you want to be linked more closely to her children who are actually your own grandchildren. That's not a judgment or a bad thing, but I am wondering about it. Also, it seems as if you are hoping to shed some light on the genetic links to health-related information such as alcoholism, and such knowledge could be valuable to your biological child.
My suggestion is to wait, simply to allow a bit more time to pass while you reflect on your own motivations. I don't think you have any particular "rights" here that would increase your value to the current parent and your daughter, and yet you pose legitimate concerns and suggest you're exercising caution in moving forward. No harm can be done by waiting a while more and getting clear on what ideal outcomes might be and how you and the current parents, at least the mother, can approach this matter with good communication and a strategy that will enhance the life of your daughter.