I am so sorry to hear that this is happening to you and your little one.
First off, please do NOT feel guilty for your partner taking her at night. You guys are a team. I understand why you feel guilty but you really mustn’t - she is with her parent in a safe, loving environment at all times. Plus it’s nice for her to have some time with Daddy!
I’m afraid I don’t have experience of having s baby with a skin condition but i suffered badly when I was a child. I don’t remember it of course (and neither will your LO!) but my Mum has told me about how hard it was.
She found (and I still do now!) that some creams (like E45) actually made me feel worse - although they helped the itch they were so heavy that they made me uncomfortable in their own way so stick to light creams where possible
Could a cool bath before bed help? I had/have this stuff from the doctors that you put in the bath and I swear by it, I’ve used it since I was about 2! Turns the water blue. It’s a good way to get covered all over without feeling weighed down, might be worst asking her GP aboutnsomething like that?
Sometimes a massage can help too - it’s the sensation of touching something that’s itching without damaging the skin with sharp nails if you see what I mean! But totally depends on how sore the skin is etc
Fingers crossed that you guys get some relief! You are doing amazing and clearly care about your LO very very much - you certainly don’t sound like a failure as a mother in the slightest!