I'm just wondering if you have ever mentioned your daughter's sleep
problems to her doctor?? The humming and rocking that she does is maybe a comfort thing? I would mention it to her doctor as well.
The only thing that I could really recommend would be to have a nightly routine that you follow before bed (snack, bath, and bedtime story, etc.)and try to put her to bed the same time every night when possible. Also, try to cut the middle of the night bottle you give her. We stopped that with my 20 month old son at 5 or 6 months when he started sleeping through the night.
What you can do is give her a bottle right before bed to soothe her if you find it necessary or a light snack. Just remember to brush her teeth afterwards.
Does she have a nap during the day?? Maybe she is sleeping too much in the day and is therefore not sleeping well at night.....just a thought.
All I can say, is it's really tough......my son is now all of a sudden getting up at 6am every morning (he goes to bed around 8:30pm). He used to sleep until 7 or 7:30 am, but I think he is getting a few more teeth and is in some discomfort. Or maybe he is just establishing a new sleeping pattern. I'm just so tired all the time!