My dh had similar frustrations with dd1. Except he was the PT employed, at-home parent, and I was the WOHP who night-nursed (well, and parented as soon as I got home). There were several nights where dh demanded that we night-wean, CIO, etc. too.
I think the last was when she was about 18 months old .... many of our worst nights related to teething.
What we did to solve it, was first to side-car the crib. Then, I made sure that I nursed on my side with dd1 in the crib -- so there was less disruption for dh. And even though I think it was counter-productive for the long term, I pretty much slept with dd1 latched on for the night -- she would nurse in her sleep and not having to wake enough to look to latch, got both of us more sleep.
[I should note that dd1 had severe reflux too - do you have anything like that going on?]
Night sleeping was rough and disjointed until dd1 turned 12 months and then it was almost like a light switch - she suddenly started sleeping through for 12 hours at a time (I kid you not). It was amazing. Then, after that, the only times her sleep was interrupted was when she was teething or sick.
I agree that it will probably work best for you and ds to sleep separately from dh. Remind yourselves that this is TEMPORARY and an investment in your child's long-term GOOD sleep habits. Whether it's figuring out a way to nest on the floor without the pets joining you, or whatever - that's probably what will work best. It COULD be that he doesn't sleep well with others, but until he's old enough to sleep through the night without nursing (and he's not ready for that yet!) .... this is what you'll have to cobble together. There were nights where dh slept in the spare bedroom while I wrestled with dd1's sleeplessness. And then other nights where I would take dd1 out of the bedroom with me, and sleep elsewhere.
Both our girls have also had a few nights in their toddlerhood where they just didn't sleep - they stayed up most of the night (not teething or ill, just awake). Those nights, I would move out to the living room with all the lights still off and lay on the couch while they played quietly 'til they were finally tired.
I don't know how much that helps ... I could add that dh is an avid supporter of cosleeping now, and while it's not like he looks back on those days with fondness, he knows that they were just part of the journey. dd1 has been sleeping alone in her own bed since before she turned three. dd2 is still sleeping with us .... but getting closer to ready to join her sister. She sleeps in the sidecarred crib next to our bed.
ETA - I know you are overwhelmed and busy right now, but if you're able to get out and make some supportive friends, it could make a world of difference for you. Have you posted in Finding Your Tribe to see if you have a fellow Mothering Mom in your area? Is there an AP playgroup, or an LLL group? If you can find a mom or two who knows where you're coming from, that support IRL can make so much positive difference. I didn't have a Mothering mom in my town until recently, and it's just an amazing blessing to have someone to talk to who "gets it" like she does.
The mom doesn't have to have a babe the same age as your ds - in fact, if she has older kiddos that might be ideal, since she'll have walked the path you're on already.
And might be more able to give you and your dh some *couple* time by watching your ds for awhile, or etc., which would probably help recharge things for you too.
