S.M.
You've probably tried all this, but here are some ideas. Comfort them and stay in the room, but not touching anyone, just saying "it's ok, shhhh" so that they don't get so upset. Once that starts to work, start leaving and say "I'll be back to check on you in a few minutes." Step outside the room for 1 minute, then come back. Say "I'm just checking on you" but don't pick them up or touch them. Then say "I'll check on you again in a few minutes". This time leave for 2 minutes (or 5 depending on how it's going) and keep making it longer. After a few nights, hopefully they won't be upset when you leave and you'll be able to just say "ok, I'll see you in the morning".
I almsot forgot. By 1, they may be ready for 1 long nap instead of 2 naps a day. Try keeping them up, feeding them lunch around 11 and then napping by 12. That may help.