This is a dilemma and it happens all the time , it looks like you may have to make sure they are okay then let them yell, I agree its tough, would it work if you put them in seperate rooms for the moment with twins one usually is the instigator,they have got used to that wonderful cuddling,we all adore that dont we, I suspect that when they yell you go and pick them up, then put them back down then they yell again...see the pattern, so dont do it, you are sending the message that you will pick them up each time they yell.I know its uncomfortable but I dont know any other way, no picking up and down....Good Luck
Could they possibly have colic or have stomach cramps? Have you called your doctor to ask for advice? Is there any family like a grandma or a grandpa to come and help for a while? Having that many children around the same age at the same time can be very difficult. I have no idea how people can raise multiples like this without losing their insanity but I am sure that you two are doing great! I do have 3 children but only had one at a time. I would highly suggest that you bring in reinforcements to help out because you sound like you do need it. Even a family friend or a babysitter for a few hours a night to get things settled may help out a lot. Good luck and take care.