Maybe it's just all my own insecurities that are passing onto DD.
I think you've hit the nail on the head. I doubt she's bothered that she's smaller than everyone else.

As for the coping with a toddler and a new born? I just took it 15 minutes at a time otherwise I'd end up on the floor in tears with both of them. Sometimes someone has to wait while you are doing something for the other child and no matter how much screaming they are doing, nothing is going to change it. Your toddler will get it eventually.

I don't think that my son understood about a baby but he knew things were happening and that's what put him off balance.