Get a carrier. Try the Ergo with the insert. Carry that baby, mama! But get those poor hands and arms free.
This way, your new baby will either get used to sleeping while you carry her around and care for your 4-year old - which is great because you don't have to tip-toe around - or you can get her to sleep by herself by this technique: holding her for longer. She SEEMS sound asleep, but babies' brains don't work like adults'. When they have fallen asleep, it is a light sleep. Go for another 20 min doing whatever works best to shut those eyes, and then, only after 20 minutes, put her down, and she should then stay asleep.
Don't make her cry it out. She is not rotten. She is in the 4th trimester. The world outside is so different and cold and motionless compared with your womb. It's traumatic for babies to leave that! It's such a scary, foreign place to her right now. You can't spoil her by holding her whenever she needs you, wants you, cries for you. Don't make her cry it out. Leaving her to cry and throw up and give up would tear away at your bond with her and you'd start to lose your sense of what she needs because, when you respond quickly to her cries, you're learning every time how to best meet her needs This is the difficult part. And with another child to care for, yes, it is hard. But if you don't go through this critical learning time, and instead make her cry it out, she either becomes clingier and needier and whinier (and it only gets worse as she gets bigger), or she learns on a deep level hopelessness, defeat and that nothing she does matters, has any effect on others, because not even her loving parents respond to her desperate cries.
She's just 7 weeks old. She doesn't know how to manipulate you. Newborns are the sincerest people that any of us has ever met. When she cries, she really means it. Give her all the love and comfort and security that she craves, and she will start to relax in a few short weeks and, you will see!, in a couple of months, she will be squirming out of your arms to look around and explore her world. This is because "she is full and wants to be excused from the table" - she has the comfort and affection and security that she needs. If you withhold that, you're in for a mess, discipline-wise and emotionally, all around.