OP, you need to start behaving like a mother to your eldest daughter.
Patently you have a better relationship with your younger child, but that really isn't relevant to the way you should be dealing with this. You are the parent here.... that doesn't mean you should have control, it means you should be old enough and wise enough to be the person who builds bridges and offers unconditional love.
Nowhere in your OP do you wonder about your daughters' emotional needs, or ask how you can mend this relationship. It is essentially a diatribe about her shortcomings and difficult behaviour. I don't hear much love in the comments you make? I don't hear any self searching about how you may have contributed to this situation? or why she may be reacting in the way that she does? Most worryingly, you don't say that "I don't like the things she does" or "I don't like the way she behaves to me" - you say "I don't like HER". That is incredibly damning from a mother. Do you think that she doesn't feel that distance, and dislike?
Does she remind you rather too much of her father, by any chance? has she inherited his personality, and spent her life being emotionally punished for it?
However much you reiterate that you worked, struggled, supported, behaved responsibly, when she was growing up......this isn't something she is supposed to spend her life being grateful for. It was your job as a parent. If you resented the life, did you make her feel that it was her fault? was she difficult when the marriage broke down, and you found it one thing to much to deal with her loss as well as your own?
I am asking these questions because you need to start really thinking about how you have related to this girl, all her life. Without the self righteous, 'its all her fault', spin that you present here. You need to be truly honest with yourself, and try to see how she may have felt about incidents through her growing up ....not how you felt about them.
Above all, you need to stop comparing her to the 'golden', 'well behaved' sister. In your own head. Let alone to her. Why are you not proud of her achievements? why are you not holding her up to your youngest as an example of how to achieve academically?
Daughters do not choose to become 'no contact' with mothers, at age 26, unless there is a history of feeling damaged. If you have any interest in salvaging this relationship, if you love your daughter (despite disliking the tensions which now exist) and want her as a part of your life then you need to stop being egocentric, and pick up the phone to your mother and tell her that the situation is breaking your heart because you love your daughter and you want to try and sort this out. You ask if your daughter would consider meeting with you, on neutral territory, just the two of you ..... not to debate or argue, but so that you can listen to your daughter. So you can ask why she feels the way she does.
And, if she agrees to meet you, then you need to go and just listen to her and take on board what her feelings really are about your relationship. Don't tell her she is wrong to feel as she does. Don't argue with her - or tell her she is wrong. She is not 'wrong' if it is the way she feels.
Just find some humility and discover what really is wrong with your relationship from her point of view Trust me, its going to hurt you.....but you need to hear a point of view other than your own.
Then, and only then, will you be in a position to talk about your relationship in the future. But remember that mothers who truly love their children keep a door wide open for them.