Agree it sounds completely normal and it will pass, you WILL get through it.
Also agree with the above poster - you're stressing too much over this adult time. You can speak to each other while feeding/holding the baby, get yourself comfy on the sofa and put your feet on H lap while he rubs them.
I know it's hard when a good sleep feels like a distant memory, you can't think straight and it feels like your DH is your No1 enemy, but try and stay positive and calm. If you feel you're going to snap or he does with you first then just say something nice or even stupid, it really can diffuse the situation and make you both laughI quite like the word pissflaps :) but obviously not within earshot of DD
when your alone with LO at home, sleep when he does. Even little naps can make all the difference when you are sleep deprived.
Let your hubby do some of the work, he will learn.
Get your DD involved (where possible and obviously if she wants to) to sit with LO, speaking/singing to him if your busy. My DSis has a 3 week old and a 7yro DD and during the day she can hardly get a look in....DD want's to help with everything,fetching changing stuff etc.. and sometimes, after dirty nappy and hunger are eliminated, her speaking and holding LO hand is enough to quieten her down for a little while.
Make a point of getting out of the house regularly, go for walks by yourself with baby in the pram but on weekends get out as a family, it doesn't matter where, a walk in the park, trip to town, the beach, anywhere but do it as a family.
With my own DC I always used to wake them 30 mins before I wanted to go to bed and feed them, regardless of when the last feed was, even if it was 1-2 hrs before. I didn't want to go to sleep knowing I would be up for another feed in 2 hrs time, so by doing this I knew baby had full tum and would sleep a minimum of 4 hours still horrific but better than 2 Once they start sleeping longer then give the last feed earlier.
Hang in there OP xxx