I'm so sorry you're dealing with this. It sounds like a really tough situation. When you are in the thick of sleep deprivation and babyhood it is so hard to feel like it will ever end or get better. I know everyone says this, but it will. My DD was never as difficult as it sounds like yours is when it comes to sleep, but I KNOW she will not still be waking up like this forever.
I also struggled with resenting my husband. He could sleep through anything, and I simply couldn't. Add breastfeeding on top of that, and the fact that he was working a demanding day job and I wasn't, and almost all the night parenting fell on me. I had insomnia--by the time she was a couple months old my whole system was so messed up I don't think I could have slept through the night even if she did.
No real solid advice that you haven't probably thought of already. I do wonder if you feel there's more your husband could do. If she's up till 2, can you sleep while he stays up with her? Can the two of you trade off night shifts?
Do you like/trust your pediatrician (I hope so!)? I don't think pediatricians are generally that helpful when it comes to sleep, but it might be helpful just to talk it out and get another perspective. Her waking patterns (at least, the staying up so late) do sound pretty unusual to me. Another thought is maybe trying an earlier bedtime--like a lot earlier--to see if that helps. The whole overtired cycle can be really tough.
I had a lot of anxiety around sleep. I don't know if that's something you're struggling with. But I did discover that I could function better on little sleep than I thought I could--it wasn't easy, but my body adjusted enough that I could limp through. I only say that because it helped my anxiety a bit to remind myself that I was managing to survive on less sleep than I ever thought possible. My DD started sleeping through the night semi-consistently around 13 months (she night weaned at that time), and truly consistently around 21 months.
She is now 2 and though I still struggle with insomnia, I feel much better rested and sane in general. I wish I could offer more concrete advice or a cure, but all I have is my support--I'm thinking of you and hope you find some solutions soon.