I feel for you as a parent. It sounds like you have a lot of hurdles . My thoughts would be to break it down into increments and see if you can overcome your daughter's reluctance to see you.
First of all, I can't help myself and I have to ask this: Did you undergo anger management counseling during or after your tirade with the judge? If not it could be an avenue not only to negate some alienation excuses and maybe help you find some peace somewhere in this mess.
Always remember that teenagers. . . and your daughter might as well be she's so close. . . are fickle creatures. They will do what they have to do to get through a situation. Since she spends the majority of the time with her mother, she's not going to want to be on her mother's bad side so she'll say whatever to keep mom happy. For that reason, you should NEVER give up. Remember that pushing you away is how she's surviving right now. Keep trying. I've heard some of the worst stories from adult children who felt one of their parents gave up on them. And it's solace for you that you never stopped doing everything you could to be a parent to your child.
At age twelve it's not the child's decision to not see a parent unless there's an order of protection. Baby steps. If you have a
court order for visitation, exercise your visitation. Send a letter of when you'll be picking up, and do it consistently. If daughter balks and you back out of the visitation, she won't view it as "whew, dodged that one". . . it's more like, "see, he doesn't want me anyway". Know what I mean? Send that letter every time you have a visitation due and stick to it.
You know what? It may take months or years for your daughter to come around. But heck, what else are you going to do? It's a lot more fufilling going through life knowing you are constantly trying then just making an attempt once in a while, or worse, not at all.
ETA: I have three teens right now. I so feel your pain. They are WEIRD and I finally feel "old".