You know K., it's weird but I have seen this a lot with second-time moms! I only have one so I don't have firsthand experience, but what you are describing seems common.
Here's my theory, based on my own experience: I was a nervous new mom, as most of us are. Bringing home your first baby changes your life more significantly than perhaps anything ever before has, or after. There is so much to learn, to worry about, to adjust to, to be amazed by. In some ways for me, this "shell-shock" partly blocked me from enjoying the first few months as much as I could have, relaxing and really listening to my maternal instincts. (I'm not sure it could have or should have been any different, and I'm not saying that I wasn't maternal, I was just insecure about it.)
I often wonder if a second child would be easier because I would be so much more relaxed and confident. Although my friends are quick to remind me that you are so tired and overwhelmed trying to care for a toddler and a baby, that this is a fantasy! But to some extent I think I would be much less nervous and plus all one's prior experience as a mom, one is less prone to just do what people say you are supposed to do. When you are a first-time mom and feel like you have no idea what you're doing, you don't question what the doctors tell you. I had every intention of keeping my son in a bassinet and never occurred to me that he'd sleep with me (in my prenatal class this was clearly a big no-no!) If things had gone differently he surely would've been a crib-baby.
Now that I've already had the experience of being a mom, I can confidently say that I wouldn't dream of ever letting a vulnerable little newborn sleep alone, out of my sight, who wants nothing but the security and nurturing of his mother whenever he/she is awake. How could it possibly be natural for a baby this young to be all alone? They want skin to skin contact, want to smell you, want your warmth and the sound of your voice. Trust me, the more of this they get, the more secure and happy they are when they are older. I think all women know this truth on an instinctive level. But our society (ALL societies) teach us to do and accept counter-intuitive things. For us, we live in a society of convenience....and it is inconvenient, on some levels, to have a child dependent upon its parents for sleep.
I know that if I ever had another baby (probably won't happen, but...) I would surely try to right everything I had done wrong with my son. He used to cry and cry and wanted to be held ALL the time, mostly by me. I struggled with this. For the first few months after he was born, in was in alot of pain from the birth and i was over-working myself, so I took a long time to heal. This made it painful for me to carry him around all the time. I still did carry, hold, and touch him constantly, but I resented it sometimes and would get frustrated. I was exhausted. I felt sorry for myself. Babies pick up on that! O well - I wasn't perfect! But if I had another baby with the same temprament, I would accept his/her need without the resentment, and make more of a "baby-wearing" effort. I imagine that we'd both be happier. That is just one example of what I mean.
I think you are just instinctively wanting to be as nurturing and connected as possible to your new baby (congrats, btw!!!) because this is the most natural, harmonious way to be. Stop fighting your instincts, do what feels right for you and your child! Don't let guilt cloud your intuition. All children have different sets of needs and also motherhood is always a little different each time around. There is no need to let go!!!!! Hold her as closely and as long as you want to, your love will not hurt her, only benefit her in every way. I wish you the best of luck!!!!