I certainly don’t know enough about you to know whether you were a good father to your kids, but I think you are morally and legally responsible for her education. First, you will probably be made to pay the bill in court. I know a few people who have found themselves in similar situations, and had to pay. One was actually a woman who had to pay for her step daughter’s education to a fancy private school because she had joint accounts and shared assets with the father.
If you were still married to your ex-wife, and/or had a good relationship with your daughter, would you have any problem paying for her schooling at the school she has chosen? If your answer is no, than I think you are being really shortsighted and selfish. You shouldn’t do things as a parent with the expectation that you will receive something back. It’s an inherently one-sided relationship for the first few decades. That’s part of being a good parent. I am also kinda surprised you spent more time talking about how it will be a financial disaster than about how your daughter was accepted (and received a partial scholarship) to a great school. I can understand the sobering effect a bill of several thousand dollars can have, but you don’t have a right to be bitter about something like this. The main issue is that your child has a desire to further her education, and do something with her life. You seem more interested in receiving her approbation and affection, then being part of raising an educated and well rounded human being. You know what you did and how you helped mold her, whether she recognizes it is irrelevant. She may think you are a asshole, but the money you give her is what will help her get a great job in the future. That’s what’s most important.
If I were you, I would stop trying to fight it, and set up and meeting with your wife where you promise to redouble your efforts, and stop making her job harder. You should apologize for making your daughter feel like she doesn’t want to be around you, and any other thing that has made the situation more difficult. Doesn’t matter if you don’t feel that way, just say it. Sometimes, being right is not as important as being happy. I would also stop asking your other daughter why the first one hates you, and just tell her to tell her sister you love her and hope she is doing well in school.
If you fight this in court, you will lose either way. If your money is more important than your relationship with your daughters, then go ahead. If not, suck it up, and and pay the bill.