Ester is right...dogs have to establish their own pecking order. Your older dog is trying to maintain her Alpha while the new pup is trying to become the Alpha. We had an American Bulldog named Chopper...he had a set of strong jaws on him hence the name Chopper.

Chopper was not the type of dog who I would have ever imagined to be able to put up with a small nippy dogs...however, when we brought a BT (Kona) who only weighed 3 lbs at the time she managed to jump on his back, bit his ears, cheeks, neck, tail...basically every part of Choppers body she could reach. Bear in mind Chopper was 86lbs and could squash or crunch down on Konas little head in a split second. Chopper basically put her in her place by letting her know what is acceptable and what is not. The only time Chopper got out of hand was when he was given a piece of bone marrow at which time Chopper managed to attack Kona. Something to always keep in mind is to try to keep an eye on dogs when giving them any raw or chewing bones.
Long story short...Kona became Chopper's best buddy and Chopper absolutely adored Kona. They would take turns grooming each other every day and Kona always knew her place in the pecking order. Sadly we had to put Chopper to sleep 3 weeks ago due to kidney failure. Kona was devastated. She lost her best friend ever. I did end up adopting 2 BT pups surrendered by puppy mills 4 days ago and I have my own set of challenges now.
I do hope this helps you in the meantime. Hope everything will work out shortly.
Marisa