9 month old twins sleep trouble

We have 9 month old non-identical twin girls, Laura and Alice. Their sleeping skills are very bad, especially in the case of Alice.

Alice cannot fall asleep in her bed. When she falls asleep in our hands or elsewhere and is then put in her bed to sleep, 4 times out of 5 she wakes up and starts to cry immediately becoming more and more hysterical if not picked up. During the night she usually wakes up once or twice and then starts to cry and we need to bring her to our bed and then when she falls asleep again (sometimes after feeding her) we have to bring her back to her bed and hope we can put her to sleep without her waking up again.

Laura behaves similar, bur the success rate of bringing her to her bed is much higher and she does not wake during the night so much.

We've tried letting them cry in their beds while only comforting them from time to time. They stop crying whenever picked up and continue crying whenever put back in their bed. It seems as if they could go on like this for hours although we've never done this for so long fearing that letting them cry too much will lead to infant depression or something. Since there are two of them if one of them cries vigorously she wakes the other one up.

They do nap once or twice during the day, especially during walks or car rides.

Either way we've completely failed in establishing a healthy sleeping routine. Instead our usual sleeping routine looks like:
9:00pm: oh, great, Laura fell asleep, bring her to her bed
9:05pm: oh no not yet, she woke up, bring her back, but no big deal as Alice is still up
9:15pm: ok Laura fell asleep again, bring her to bed
9:20pm: ok Laura is soundly sleeping
9:30pm: oh great Alice fell asleep, let's wait 10 minutes then bring her to her bed
until 11:30pm: trying to bring Alice to her bed when she is sound asleep and bringing her back to comfort her when she starts crying in her bed
11:30pm: success! the babies are both asleep! time to sneak some sleep hours in.
3:00am: Alice wakes up, gets some breastfeeding, is brought back to bed once or twice unsuccessfully, often wakes up Laura as well for additional entertainment
4:00am: both of the babies are sound asleep again!
6:00am: the babies wake up and declare they've had enough sleep, starting another productive day of attacking every wire, shoelace and prohibited household item they can get their teeth on

It used to be better in the sense that they didn't wake up during the night, but they both caught a cold about a month ago and started to wake up very frequently due to congestion. The cold passed but the habit of waking up during the night didn't.

Any ideas what we can do to improve their sleeping habits?