((HUG)) Having a new baby is draining, even if she is the most cherished baby in the world. You are tired and overwhelmed right now - any of us are with a newborn, whether our first or our fifth. (I just got home from staying at my best friend's house, helping take care of her first four while she recovered from the c-section she had to have to bring number 5 into the world.)
First, your feelings sound dangerously close to post-partum depression, which is a condition that is treatable - it is a chemical imbalance, not a character deficiency. Talk to your doc about how you are feeling, and don't be afraid of taking medication for awhile if it proves necessary.
Second, now is the time to call in the cavalry - extended family if they are the type who are actually supportive, friends, your church, your neighbors. One of the hardest things for many of us is to ask for help if we need it. After all, we "should" be able to handle it all, right? :-) Your friends would love to help you. They are probably waiting for you to tell them what you need. So don't be shy about asking for playdates for your other girls, meals, a clean kitchen, someone else to watch the kids for an hour so you can grab a nap... These are things that can help restore your spirits and allow you to better cope with the demands of a changing family.
Also, talk to your kids - your oldest ones are old enough to understand that your attention and energy will, out of necessity, be focused on the newest family member for awhile. Tell them daily that you love them, that you appreciate their patience, that their efforts at helping out are seen and appreciated. Ask them to help out as they are able (perhaps your 8 year old could help with those thank you notes?). School will start soon for the older two, thus restoring a little normalcy and routine to their lives. And maybe a little less clean house in exchange for 20 minutes with your toddler to help her feel loved is a worthwhile trade-off?
Where is your spouse in all this? He can pick up the toilet brush, dust, cook (or microwave frozen things), spend time with the toddler and older girls, or pick up some of the other family responsibilities you usually handle. Right now you are still recovering from giving birth and dealing with an infant. He can (and should) step up as your life partner. When my second was born, after a complicated pregnancy, my husband gave my then-3-y.o. the gift of his time. He had a heavy work schedule then, but every evening he took time to play with her and read to her, as well as handling bedtime. (I dealt with the colicky screaming baby.) The bond they formed then is still special and strong today, seven years later.
Your level of guilt makes me concerned for you. It is unrealistic to expect to be mommy perfect 3 weeks after giving birth. The baby weight takes at least half a year for many of us. My doc told me not to make love until at least 6 weeks after. Please forgive yourself and give yourself time. You are not doing your family permanent damage! Such intense transitions as a new baby in the family are a part of life, and coping with them as part of a loving family will help make your girls into adaptable, resourceful people.