She might be more clingy because of the new child and also daddy being gone. If you stay up with her and comfort her to sleep you she might not only regain her confidence and calm down soon, but also the baby won't be awoken. The best parenting book I've ever read is William Sears' "The Discipline Book". The third chapter is called 'Understanding Ones, Twos and Threes'. It is full of compassionate solutions and made parenting a thousand times easier for me. I really think my child is calmer, more affectionate, sympathetic and better behaved as a result of reading his books.
Contrary to popular belief, I do NOT think this is a power struggle or that she is trying to control or manipulate you. I think this belief has lead many parents to develop defiant and oppositional children because the children are not getting the love and comfort they are plainly asking for and needing, but instead the parent is introducing this conflict with them. Recent studies show that the best way to foster independence is by comforting children until they are ready to separate, and that forcing a separation before they are ready leads to insecurity and dependence. (See "The Yale Child Study Center Guide to Understanding Your Child")
I've read over a hundred of pregnancy & parenting books and concluded that the more you nurture and "indulge" your child (and it is never too late to start), they easier they will be to parent for the rest of their lives (and this includes better teenage years!) Good luck. :-)
P.S. Taking care of a toddler and newborn with a body that is still recovering from childbirth (and it takes an entire year for the body to fully recover) would seem pretty near impossible for a single person to do alone. I would hope you could receive plenty of support from family, friends, community, or even hired services. I doubt anyone in your situation would be able to fully care for their children and themself in the way everyone needs to be cared for at this point, unless that person were getting TONS of help. Mother's health and happiness is very important for the whole family!!