You poor love. I've been where you are and the world becomes such a spiky hostile place when you've had no sleep for weeks.
Deep breath.
I don't see your DH being an arse. He packed the car and was willing to go. MIL persuaded you. As PP said sagely above, don't be persuadable. Find your No. A nice firm round No. It will stand you in good stead for life. Don't be a martyr. The situation is shit but there is a lot of power in taking charge of your needs. Power to YOU that is. I understand that right now when your eyes are burning with tiredness it seems so surreal but it's all within reach and you can do this next time.
I've mix fed successfully for a year. Now you've established BFing, introduce a bottle in the evening so you can hand over to DH and get a break. It was a life saver for me. I hated expressing. My DD was still classed as exclusively BFed by the GP 
The arguments about how much sleep you each had are pretty standard. Having spoken to a lot of women about this, the most loving supportive couples have had this or a version of this. I used to call it Tiredness Olympics
"I had an hour, and I had 45 mins, type of thing. Sleep depravation does really odd things to our brains and distorts everything. Don't let this temporary thing change things permanently between you and DH.
Get MIL to take baby this morning, let them take DD for a walk after feed, have a hot bath and go for a nap upstairs. And when you get home, get some earplugs. I found that when DP was around with DD and I wanted to nap I could hear every noise. Partly sleep deprivation partly the instinct of always being watchful. Once you get your rest, give your DH a hug and tell him that you love him.
Take care my lovely. Many have been where you are now and came out on top. FWIW I really disliked the baby phase intensely. DD is 20 months and it does get better.



