Sounds really hard. Hmm. I don't have twins, so I no I'll probably get people saying it's not the same, but I did have a small gap between my two..so at the newborn stage I also had a 17month old baby wandering around, tantruming, waking in the night still etc etc. And no, not old enough to help by bringing wipes or anything!! So I do recognise the complete stage of sleep exhaustion you are describing. Two lots of crying at the same time is just horrendous.
I also massively struggled to get out of the house - 2 small ones on totally different schedules, so I don't think that's limited to twins (and also I lived in a top floor flat with no lift - that really didn't help!!)
How do you cope? One day at a time. Lower your expectations. Ask for help - don't expect people to just offer it. Tbh, I got really low because i couldn't understand how my friends were ok with me really struggling and no one was offering to do anything. I think with hindsight, I should have just blatantly said I wasn't coping very well. I cried a lot to the HV but never to any of my friends. How silly.
Don't clean or do any of that crap. Leave it for husband to do or buy in some help.
The early days are horrendous frankly, doesn't matter whether it's your first, your fifth, twins or triplets! Oh and that is my other tip. I tried to think of people who had it much much harder than me ( a lady i know who had 2 yr old twins and THEN another set of newborn twins!!!) and thought, actually, come on, you can do this.
Do you have homestart in your area? Ask now for help. They finally sent someone to help me, but it took 3 months after I asked - at which point I was finally coping so didn't need it any more! They will help with any multiple births or multiple small kids in a house.
You're not alone. Mind you. Mine are 1 and 2 now and most days I'm still in bloody tears not coping particularly well! Except now it's different challenges!!! One day at a time. And ask for help. Help off ANYONE AND EVERYONE!!!