Hi OP, sorry to hear your LO isn't sleeping well.
As mad as it sounds, my DS sleeps and goes to sleep better if we catch him before he gets too tired. What I would do is whatever works for your dd to sleep during the day is just do it, then at night time, have a bath, then a feed, then bed. Try putting her to bed early at 6pm and see if this makes a difference.
At night time, I would wait until she is settled/not crying and put her in the cot with socks on hands, even if she is awake but not asleep, leave the room and if you don't hear any crying, wait for 10-15 minutes and then go in and check. Sometimes I've accidentally disturbed DS trying to get to sleep on his own by going in to check him. I think sometimes if you spend time trying to sing lullabies it just wakes them up rather than settles them if they're not unsettled or crying.
Our DS rubs his eyes and scratches his head when he is tired. He is too wriggly to be swaddled now, so we put him to sleep on his back in the correct position and put socks over his arms (as scratch mitts are too small!), this has helped a lot as he's not fulling waking himself up with scratching and he doesn't have a bleeding head anymore!
A few weeks ago he wouldn't sleep during the day at all and it was awful, I did two days of putting him in his cot for an afternoon nap after his lunchtime feed and I was determined he would sleep as he definitely was tired. I put him in the cot and let him cry a little while and picked up up after 5 minutes for a cuddle to stop him crying, then put him straight back in the cot, I had to repeat it three times so he cried for a total of 15 minutes, but he suddenly gave up and fell asleep and slept for about an hour and a half.
I don't know if this is classed as controlled crying, but I did it for two days (afternoon naps only) and it worked. The way I see it is if I was bursting for the toilet and he was crying I'd have to leave him to cry for a couple of minutes, or if I had other children he might have to wait a couple of minutes, and babies do cry so I don't think it's too awful. Anyway, this worked on the afternoon nap after two days, I put him in the cot and he just went to sleep on day three.
I can only say this is what I do/have done and all babies are different, so it might be worth a try.
Also my DS tends to sleep better if we are out and about e.g. In the pushchair or the car. On the rare occasions he's cried in the pushchair or car it's been because he needed a nappy change. I think fresh air helps.
The other things that has helped DS is being introduced to solids, he was waking up around three times a night just plain hungry and milk alone wasn't cutting it. My HV was dead against introducing solids before six months, whereas my gp said introduce solids anytime after four months "when the feeds are becoming too frequent to manage". I know a lot of people on MN are against introducing solids before six months, but I think you know if milk is not enough anymore.
The last thing that has helped my DS sleep better at night is that he can now roll, so he always sleeps on his tummy now, I was worried at first, but if they can roll onto their tummies, the SIDS risk is lower as they can roll back or to safety if that makes sense. He definitely sleeps better on his tummy, although we always put him to sleep on his back!
In the last two weeks or so, DS now naps for approx two hours in the day, usually half an hour in the morning and an hour and a half in the afternoon. He now sleeps through the night, the times varying, but he generally has been sleeping at least 10 hours, up to 12 hours with no waking up.
Anyway, I don't know if this has been at all helpful, but good luck! I hope things improve for you!