A.C.
The big part is you need to be consistant. If you start one idea, you need to follow through with it for as long as it takes. You can't try it for one day and then give up and say this idea doesn't work. I'm sure you've done everything you can think of, but by all means that does NOT make you a bad mother. You do all you can and that's just fine. I leave music in my daughters room all the time, 24/7. It's consistant and peacful. Plus it becomes familuar so if they wake up, they recognize it and can settle themselves back to sleep. My big reason for doing this is for noise, so she doesn't wake up to everything.
Also, if you try rocking her make sure you are as relaxed as possbile. Babies can feel every tension and stress in your body. And DO NOT make this just a mommy routine. Daddy needs to try and participate in this too. You cannot do it all alone; your life and well being cannot be strained for this long.
Any items she really likes, or positions she likes to sleep in at night (on the side, on her tummy) then let her do that. My daughter would only sleep on her tummy even as a newborn, and she wasn't happy unless she was laying on my chest all the time. Plus, she absolutely hated her carseat: that's a whole other story. Your daughter is old enough now to be able to control rolling on her side, so if she likes it and let her do it. If she acts like she wants a bottle, give her water (and if you can try to get her used to a sippy cup it's easier so you can leave water in her crib without it spilling). You may have started her on baby foods now, if not then she is ready. If she wants a bottle every 2 to 3 hours then she isn't getting enough food and needs something more solid to fill her up. She could used 3 meals, with formula as a snack inbetween, and even in the middle of the night. She could have a hard time sleeping because she is always hungry.
My daughter didn't used to sleep more than 20 mins when she was only a month old because she didn't like the basinet, always wanted to be held, and wanted to be on her tummy all the time. Once I discovered the tummy thing, then she began to slowly sleep longer and eventually like naps and consistantly took them everyday. So, try a new position.
Some babies just have high anxiety and can't sleep well at all at any time. It's unfortunate, but as long as she has relaxing moments, just as sitting with you rocking and reading a book, she will be getting some rest that will help her. Even taking more time before nap time getting her ready to sleep could help. Take more time reading, then singing, then humming. The key is to lay her down when her eyes get heavy so she can fall asleep on her own. Her body needs to feel heavy, which triggers a chemical in the brain that tells the body it's tired. They also, make weighted blankets (which can be very expensive) that can help children fall asleep. I would consider this as a last resort.
If she still refuses to sleep, then just have several resting periods a day (probably 4 times, or more, depending on exhaustion. This could help her with crankiness. She may not need a lot of sleep time during the day. Some kids have more energy and don't need them.
One more thing. Has she started teething? If not then she probably is now. My daughter started at 2 months but they didn't start popping through until 6 months. So check the gums for flat spot on the bottom (bottom teeth come in first, usually), and you may even see little slits in the gums where the teeth will come through. My daughter had a hard time at first and I couldn't figure out why she was so cranky, which makes sleeping harder. I tried teething tables and little drops of Tylenol occasionally and it made all the difference. She was uncomfortable and I didn't know it. If your child has been sick at all this season, you could also have her checked for ear infections. I watch a 7 month old and all he had was a stuffy nose, and then followed by constant crankiness and less sleep. Come to find out he had a double ear infection. You just never know what it might be.
Hang in there, and help your husband to understand the stress and maybe he could help relieve some of it from you to allow you to take a bath and gets some much needed relaxation of your own. Your daughter won't stay this way forever, and keep reminding yourself why you had her and you will get through this in no time. I always told myself, "This is only a moment compared to a lifetime."