K.P.
There were times when all three of us just sat on the floor and cried. Then we picked up the pieces and went on.
One tip is to have a baby carrier of some sort -- a sling, front-pack, back-pack, whatever -- so that you can carry the baby while still tending to your older child and taking care of the house.
It's normal for the older child to suddenly become completely helpless, particularly when you need her to be the most helpful (or at least to amuse herself or not be so needy). She's just going to have to learn that the world does not revolve around her, and that you cannot always drop everything and tend to her. Don't feel guilty about this!! It's a good, character-building exercise for her -- far too many people remain in the selfish toddler stage even while they're adults. :-)
She will learn and adjust, and so will you. Tend to your baby, but that doesn't mean you always have to jump up at the first hint of a cry, either. Obviously your younger child's needs are more immediate, but sometimes "tell the baby" (for your toddler's benefit) that you need to finish reading this page before you can do whatever.