Hi J.
Being a new first time mother can be very overwhelming. I too felt the same way with my first child. I felt like I had no idea what to do, but it comes in time as you get to know your daughter better.
Personally, I never followed any books. I have read some, and get some info on line, but you have to realize every child is different and has different needs. You can take the info you get and apply the parts of it that you decide to for your daughter.
I found I never had either one of my kids on a good solid food or sleep schedule til they were at least 6mo old, even later on the sleeping habits with my first one.
Being a SAHM is a huge advantage, I know you are very tired, rest when the baby naps, so you can have energy when she is awake for taking care of her. Let other things go, for now and concentrate on the two of you.
I would let go of the calculation of how old your babies is cause she was 4 weeks early. My son was 2 weeks late and it never made a difference.
Is there any way you can get that 6pm feeding closer to 7pm? I would continue to feed her every 3 hours like you are doing, if she does eat at 6pm, I would still wake her at 9pm for a feeding, then put her to bed for the night, or for as long as she will sleep. Once my babies were 1mo old, I wouldnt wake them during the night for feedings, she will wake you when she is hungry. But during the daytime hours, I would wake her to feed every 3 hours, so that she gets enough ounces to hold her through the night.
As far as putting her to sleep in her bed........ Of course she needs snuggling, and soothing from you. I would try to put her into her crib after that still awake yet drowsy, but if that doesnt work, then hold her til she is asleep. She is still very young, let her call the shots for the time being. It is such a big adjustment for little ones when they come out into the world. Believe me, I've had nights and nights of crying babies, and those that didnt want to go down to sleep. Nothing is going to be perfect and on schedule for a while........ In a few months you will see things are going smoother...... Just try and relax and enjoy your new baby girl, before you know it, she will be eating grilled cheese sandwiches and you will be planning her 1st b-day party!!!
Have fun, please email me if you like
~K.