I had a similar problem years ago. The shelter said the yellow lab was a wonderful dog, loved everyone, etc. When we had her home a few days I notice she would stare at my son then about 3 years old in a menacing way. Then one day as my older Greyhound was just walking past her she struck out and tore the top of my Grey's head badly. She went back to the shelter that day with a warning that she should not be placed in a home with other dogs or kids.

are you taking her on walks, active walks that tire her out? my experience has been that bored, worker breed animals get territorial and snippy when they aren't keep active. she does sound like a child who is afraid they aren't loved so pushes any competition aside. i like the idea of also getting the two of them playing together with you. When you make decision, think of what breeds are dominate in her and whether you have taken that into consideration when you work with her.

do you have any history as to why the dog was surrendered? how long have you had her?

I know when I got my doxie rescue last October, he was very determined to be alpha leader. He had a real attitude problem. I worked with the foster mom and she helped me get through to him. Within about a month, he turned around completely and now the greatest little guy in the world.

Dogs don't understand why they are being shuffled around from home to home so some will act out. Doxies are known for their attitude issues but they are also very loving and loyal little companions.

What kind of dog is it (if you know)?

I don't know if it will work in this situation, because a lot of 'dog behavior ' includes things that can't be realized online. When that happens around here, the 'victim,' your original dog, gets the attention, praised for the way it handled it. This does 2 things, it lets that dog know it gets rewarded for not fighting, it lets the other dog know that whenever it does this, it does NOT get attention, but the other one does. It's whole purpose for getting after the original dog is to have you to itself, so it's behavior is actually having the opposite affect.
It's very important that you do NOT pay ANY attention to the new dog when it does this, and if and when it does coexist with the old one, even for a brief second, it gets praise too

This is why it's important to NOT scold the offender, because scolding attention to him is better than no attention

Cookie, my Chihuahua is like that also, she drove my old Poodles nuts until their health declined and I had to have them put down. We were her 2nd or 3rd home, I don't think anyone tried teaching her anything. I would like to get another dog but, she would take over, she is going on 5, doubt I will outlive her so I can get a breed I like better. My Husband has really taken to her.

Have you talked to your vet about this? I just find my vet to be so helpful with any problems I have ever had with my dog. It would be really sad if you had to take her back but it also would be a shame to make your househld miserable. I'd talk to my vet before I made a final decision. Good luck... let us know how things turn out please.

One other thing, we have to be careful to not put our own feelings in our dogs. What I mean is, the older dog walking away, and not being confrontational, is the way dogs are. Someone has to be the alpha, they both say the new dogs is. He is still growling at the old dog because someone there doesn't get that he's alpha and he still has to prove his place, could it be you? Sure to us people, that doesn't seem fair, but in dog-ese, fair doesn't count. If they are both happy with the new dog being the alpha, who are we to not go along with that?

Start treating the new dog like it is alpha - feed it first, pet it first. They are working out their hierarchy, it will only cause them more stress if you don't respect that. They will be much happier if you honor what they are working out.
They are going to be happier if they know their place, and you do too.

The older dog does not mind not being the alpha, as long as everyone in the pack knows it too. You are extremely lucky the old dog just walks away. The problems will start when you give signals that the old dog is trying for alpha, then there may be fights

There is a lot of information available online on training dogs. You might not be interested in a long obedience training routing, but I bet you can find the basics to reinforce good behavior. Good luck with her. She needs you for sure and your elderly pet also deserves not to be displaced. Here's a link to a short article about just what you're talking about:
"How to make your new dog's adoption work for life".
http://www.dogsindanger.com/HowToMakeAdoptionWork.pdf

Sounds like you have to show her who the alpha is....YOU.....I have four dogs....all rescued....My middle one thought she was the owner of me and everything around me....I had to put her on her back several times when she started acting out. By doing this it shows them you are the boss, the alpha. You must show them you are the boss. It may take a couple of times but she will learn fast that there is only one boss and it is you. Don't give up on her.

YOU are absolutely the ALPHA......dogs are pack animals and when we bring them to live in our homes, in their mind we are part of their "pack". If you don't assume the position of the Alpha you are sure to have problems. JMO