Both my babies were like this. Breastfed babies shouldn’t be so windy and gripey, right? Apparently, wrong.
You cannot function in an hour or two of sleep. It is hazardous. You must NOT drive a car, under any circumstances, on that amount of sleep - try telling your very risk-conscious DH that, it might make him realise you need a new plan.
I did the safe bed sharing thing for a bit with baby one, and a bedside crib/bed sharing blend for nights with baby two.
My first baby loved to be swaddled, in a stretchy knitted blanket, just to stop her reflex of throwing her arms and feet and waking herself up. After a month she only wanted her arms swaddled. I stayed watchful, and the swaddling never became an issue - once she was strong enough to wriggle free, she basically outgrew it and wen into grobags.
At 3.5 months she went in a cot in her own room, too wriggly to stay in my bed. (She needed rocking and patting to sleep though, which basically destroyed my back. )
You need to have a calm chat with your DH, I appreciate he has seen the worst, but it starts getting dangerous for you supervising two kids on so little sleep and at some stage you WILL fall asleep with your baby in your arms if you try to carry on this way. He is being unrealistic and together you have to make some real-world risk trade offs.
I followed safe bed sharing advice. DH slept in another bed/on sofa. Removed duvet, I wore warm close fitting cotton pjs and kept the bedroom warm but ventilated (high oxygen levels and a light breeze/airflow considered important for avoiding Sids, I read somewhere). Tight fitted sheet. No pillow near baby. Slept with one of my arms curled up round above baby’s head so I couldn’t roll. Slept poorly for an entire year - in my experience you do NOT fall into a deep sleep when you bed share with a breastfeeding infant, and because you are overall less sleep deprived (still absolutely exhausted, but not suffering like you’re drunk on tiredness) you are able to keep a level of semi-alertness. Psychologically you can’t relax because you are terrified of Sids or rolling on your child so sleep is not great, but it is enough. Biologically and physically it is too uncomfortable and you never really switch off. But you can drift in and out of sleep, feeding is much less disruptive as you don’t properly wake up, that way you can string together the hours of broken sleep, enough sleep to function.
I am not saying you should aim to bed share indefinitely but maybe just to get yourself through the next few months, then you can train the baby to go in the cot once you’ve got your mental capacity and physical strength up a bit.