floppops, you sound as if you're having a dreadful time - I do feel for you.
I would agree with everyone who's posted about overtiredness / overstimulation. Our DS is now 10 weeks, but we realised a while ago that he had been chronically overtired since 2 weeks old, but we were unable to get him to sleep enough to make up the backlog.
We've started using a sling (this one) during the day and he has begun to sleep more and more. Having caught up on some of the backlog of sleep he now will yawn and do grumbly cries when he's tired, whereas before he would flip straight from wide awake & cheerful into overtired yelling, so I can tell we are making progress.
We find that if he gets overtired and takes a long time to get to sleep, he will only sleep for about 30-40 mins before waking up again. Your DD may have a similar problem, I suspect. DS always seems cheeful and alert when he is chronically overtired (until the crying starts). He can only cope well with being awake for about 45 minutes before he starts needing to be helped to sleep again, but left to his own devices it can be 2 hours before the cheerfulness stops and the crying starts.
I found that if I grabbed him when he was just waking up, I could often rock/shush/pat him back to sleep. Might be worth a go to try to get her to sleep for longer periods.
Get grandparents, visitors etc to come and wear her in the sling for a bit so she can get some sleep and you can get some rest. Take turns with your DP - one wear her in the sling, one sleep. It took DH a while to be able to send DS off in the sling, but going out for a walk rather than jiggling about indoors seemed to do it. (I find that wearing the sling so much hurts my back, but I try to spend as much time as possible sitting down and am hoping that he will soon be able to sleep without it.
Some not-too-irritating white noise to try: here
I do hope it improves for you soon.