Well you described what our situation was almost perfectly, so hopefully I'll be able to help you out!
When my boys were 18 months old, I did the original night-weaning. Dw was away, and I still coslept with the boys, I just said, "no more nursing." They cried a bit, but nothing terrible, and they were in my arms, so I felt okay about it. After three nights, they stopped asking to nurse when they woke up. They did not, however, stop waking up. They remained night-weaned (yet still night waking) for a couple of months, until the first sickness came along (I nightweaned them at the end of summer), and then we were back to night-nursing. Or, the "no-nursing" time just got shorter and shorter, until I found the only limit I was setting was "no nursing before 4:00 a.m." which I think was really confusing to the boys. Basically, I was just tired, and giving in to nursing because it meant I could keep sleeping. I didn't think they'd ever stop waking up while they were in our bed. We were living in one big room, and while I felt like the boys would really benefit from having their own sleeping space. . . none of us had our own any kind of space. So, we decided to move.
We moved into a house with two bedrooms a week after Luke and Jaz turned two. In their bedroom, I set up twin beds with guard rails (they were able to climb out of the crib (we had one full of stuffed animals, though they never slept in it) from about 12 months, so I knew there was no point in putting them in cribs), and we made a semi-big deal over how they each had their very own bed. Luke had actually just gotten out of the hospital after having surgery to remove chunks of peanuts from his lung (he aspirated), and was still pretty wheezy and I wanted him in our bed. He was night nursing again too. So, at first we just focused on getting Jaz to sleep in his new bed. When he'd wake up in the night, Lena would go to him, but wouldn't bring him back to our bed. After a few nights, he was sleeping through the night. After about a week, we moved Luke into his bed, and I would go to him when he'd wake up. This didn't work out quite as well since I ALWAYS fell asleep in his bed, and then it was just like we were cosleeping still. So, Lena took over, and although Luke protested A LOT, I felt fine about it. Lena would get upset and say that she felt like she was a horrible person keeping him from me, but I just reminded her that she was his mom too and that she loved him and he loved her and he was perfectly safe, and there was no reason for her to feel bad about it. After less than a week of Lena doing the night-parenting, both boys were sleeping through the night in their own beds. They would come downstairs around 5 or 6 and get in our bed and nurse.
We still cosleep with them in our bed during sickness, but they are completely weaned now. We go through periods of night-waking, but for the most part they sleep through the night, and it is so lovely.
So, here's what I'd do:
2. get your twins their own beds in their own room (I'd skip the cribs since they'll be able to climb out soon if they can't already, and because with a twin bed, it's more comfortable for you to lie with them)
3. go to them in the night, don't bring them back to your bed
4. have your dh go to them in the night
Mindfully mothering SIX kids (ages 6, 7, 8, 10, 12 & 12) in a small house with a lot of love.