At the risk of writing a 10,000 word essay on pack behavior...I'll try to explain.
Dogs are pack animals and they operate with rules of the pecking order. YOU as the owner need to be the alpha dog and act accordingly for your status in the pack.
A) That means you feed the dogs. You make them sit before you place their dishes down. You never free-choice feed a dog for this very reason. The dog needs to know he has to rely on you to get food. If the food is always available he doesn't need you.
B) Even though you are the alpha dog and they see you as their leader, there will be a pecking order amongst themselves. Females tend to be more aggressive and challenge for position much more than males will(neutering/spaying does not effect pecking order behavior).
C) Your other two dogs are threatened by this new comer to the pack so it will take time before the new dog is accepted, that is just the natural order of things.
Now, what can you do to help things along a bit faster? With the two dogs you have, which one is boss or...which one do you allow to be boss of the other one?
Let's say you have let the female be the boss of the other dog. Okay, now, when you feed the three dogs you need to be careful of the pecking order. She needs to be fed first, then your other dog, then the new dog. This way the dogs aren't upset by you showing favor to the newcomer over them and then they feel their position in the pack threatened and will act out towards the new dog.
Same goes for when they go out to potty...the boss dog goes out the door first, followed by #2 and then #3. When you are grooming or just petting the dogs, you always call the boss dog over to you first. Same for giving treats...boss dog gets a treat first (after being made to sit for it) then dog #2, then dog #3...and all dogs being told to sit for their treat before they get it.
Besides reinforcing to the boss dog herself that she is boss of the other dogs, this also shows the other two dogs that they are not the boss and they will behave accordingly.
Trust me on this, it works. This is also why if you have an aggressive dog, you never want to let that dog sleep with you because then the dog will see himself/herself as your equal and you always need to be the alpha. In the wild, the privilegde of sleeping by the pack leader is exclusive and elevates that dog above the rest of the pack. Always make an aggressive dog sleep on the floor or in his/her own bed...never with you. This can also lead to the dog thinking that your spouse is challenging for pack position and the dog can become aggressive towards your spouse.
I have four dogs. One dog is much more timid than the others and I have made her the boss dog just so the other's don't eat her alive with their antics. She is always fed first. She is always the first one out the door and the first one to come back in. She is always the first one to be petted. Because I treat her as the boss of the other dogs they in turn see her as their superior despite her extreme timidness. I do have another female dog who will occassionally get snippy with the boss dog but I squash that behavior immediately and then fawn attention on the more timid dog just to reinforce the pack order.
If you make you dogs behave like I have described, they will naturally behave according to their status. The boss dog will be the first one ready to eat and the other's will stand back waiting to be told to sit. The boss dog will go out the door first and the other dogs will wait for her to go without having to be held back, etc. etc.
You have to think like a dog. But please, don't smell like one!
;-)