My oldest son did not sleep well until 14 months so I feel your pain. Sleeping through the night was the three hundred pound gorilla in the room which my husband and I stopped discussing. Once our son was actually sleeping through the night, we didn't dare mention it to the other person for at least a week. The fear of jinxing ourselves was strong. I distinctly remember the agony of long hard sleepless nights.
Sleep training didn't work well with my son. However, I do recommend you explore the various options out there before ruling it out. For my son the sleep training methods made his sleeping significantly worse in spite of our dedication and consistency. I mention this failure of sleep training to work because people hold sleep training up as the silver bullet. When it doesn't work, though, your exasperation can set in and you can feel like what the heck is wrong with my kid. An attitude which is not helpful. After asking around our circle of friends and family, there were a small number of babies who just didn't get on the sleep training wagon.
Once we realized sleep training wasn't working, we abandoned sleep training in favor of focusing on fostering sleep. We chanted 'sleep begets sleep." A mantra which held true when he wouldn't train and got less sleep and was harder to get to sleep. Each night was worse than the last. A vicious cycle of progressively less sleep.
Our approach was multipronged but centered around sleep for everyone. First off my husband and I traded nights. Mostly my husband took the night duties but it wears on even the most stoic. As well rather than bringing our son into bed with us, we set up a mattress in his nursery. The mattress meant the adult could get a decent night's rest. We didn't have our son sleep with us but we held his hand through the crib while sleeping and/or resting. We were prepared to sleep with him but it wasn't necessary. Finally we did feed him. He was clearly hungry and after discussing it with our pediatrician, it seemed a silly battle to fight. If we fed him, he went back to sleep easily. If we put water in his bottle or denied him food, the problems escalated and he fought that much harder to go to sleep. He weaned himself off night feedings at about 12 months.
If one of your twins is sleeping well but is being woken by the other, then I would consider separating the children. You can probably soothe one easier and faster without the stress of waking the other twin. We found bringing stress into the nursery always made the problem worse. In fact we reminded ourselves to take a steadying breath or two before going into the nursery.
I don't have any good advice but start by getting some solid sleep. Problem solving is much easier with a good night's rest under your belt. Good luck.