OMG, I could have written your post. In fact, I think I did write one just like this. My son had terrible 3's. They were really tough for him, and me. He was exactly as you describe your daughter, although his tantrums didn't last as long as you describe. But all the triggers were the same, mostly some kind of frustration about something he couldn't do himself, etc. And he would never allow me to help either, no matter how I approached him or his problem. If I even started to tell him how he might solve his problem, he would tell me, "NO, don't say it!" before I could even get the words out.
It does take it's toll. And I'm a single mom, so I got the brunt of this, much like you. As for your situation, with her not doing the same thing with her dad, I'd chalk that up to how we test limits the most with the people we trust the most, so in that way, you can take a little comfort in the fact that she feels safe enough with you to push to this degree.
The only thing I was able to do when my son would meltdown, was send him to his room if we were home, with instructions that he was not permitted to come out until he was calm, and I had described, in detail, on many calm occasions, what I meant by 'calm', i.e. no crying, no screaming, no huffing and puffing, etc. Or if he did it in a store or something, which he did, he had to sit in his car seat until he was calm. And that was my only approach to combating his meltdowns. There was no stopping them, the only thing I could do was basically save my sanity.
As for what worked, I'm not sure you will want to hear this, but nothing. He had to mature out of it. He just had to catch up to himself. Now, at 4 1/2, he is the sweetest, most lovable, well mannered, well behaved, disciplined, active, and humorous boy. I can take him anywhere, do anything with him -and want to have him with me all the time. He will allow me to help him if he needs it, he will help me if I ask, and he is getting much more competent on doing things for himself successfully. I have come to believe that it's just really a combination of consistent parenting and discipline, maturity, and physical development. Basically, the stars have to align.
Best wishes to you. I definitely know from experience what you're going through. And I got lots of responses to my post from other mom's who knew exactly what I was going through from their own experience. Hopefully, it helps to know that you aren't alone, and that your daughter is not off the deep end and there are many other kids out there like her, who have come through to the other side! The Happy Mom Side! It sounds like you are doing everything right. Keep doing what you're doing and she'll get there!!! HUGS!!