Some of it is just the fact that your DD is 2, and Deb K is right the 3's are much more trying!
We have 7, 4 of them are teens and the other three are 6, 4 and 22 months. One of the things I learned with all of them but mainly with the younger ones is this...
You have to allow the baby to come second at times, it is very hard but by answering your 2 year old first, it shows her that the baby has to wait also. This is VERY important at this age, they need to know that they are just as important as the baby, if you make her wait all the time then she is always coming in second. If 2-3 times a day you come to her first a lot of it resolve itself in time.
Get a double stroller, or one of thoses ones that have the toddler seat in back, so that when you are out you can put the baby down to meet the needs of your toddler.