Why is my dog jealous of the new dog? How can I stop the fighting?

A few thoughts here: first, esteemed PhD level animal biologist Ray Coppinger debunked the "alpha" concept when it comes to dogs several decades ago, but the idea seems to persist for some reason. Second: you should always introduce a new dog to existing members of your canine household on neutral ground. Bringing a "stranger" into your home invites territorial behavior. You don't say how long you've had the newest dog. If it is a short time, they may be working out dominance issues and, as long as no one is getting hurt, this can be okay. Sometimes, there is more noise and posturing than anything really serious going on. Not being there, I can't know for sure. If you are really concerned, or if blood has been drawn, I would ask your vet for a recommendation to a canine behaviorist (NOT the same as a dog trainer!) for help. Good luck with this!

Pack dynamics aren't really a thing with dogs, (it's a construct of wolves kept in captivity) so it may be that they are still in the "settling in" period, especially since you didn't mention how long ago you added in the third dog. Adding in a new pet can be stressful for even the most socialized and well-behaved of dogs, and as they try to determine what the new dog is like it may lead to scuffles. If they become upset, agitated or try to get away from each other, separating them all for a while in a time out and letting them relax before reintroduction can help. Removing items of contention such as toys, bones, treats, bedding, etc can also help to reduce any fights over these items. Pheromone diffusers placed in the house can also help reduce tension between new pets. Dogs are also very good communicators, so if one of your dogs hackles or growls, it's a sign that it is time for a time out period. You shouldn't scold or reprimand your dog for this, as that can lead to behaviors where they don't give warning prior to a fight. Instead, calmly just remove the dogs to different locations and try again later. If the problems continue even after a few weeks of being together, or seem to ramp up in intensity even with changes, seeking out a trainer or behaviorist in your area that can help you in person is best.

I hate to hear this is happening. Unfortunately, it's impossible to know how best to advise you without being able to read the body language of the dogs. It's possible this is occurring because they are maturing. Both dogs also need to be spayed/neutered because this can help to decrease aggression. Intact dogs are much more likely to fight and have problems. Canine aggression is a complex behavior as it can stem from dominance, possessiveness, fear, anxiety, resource guarding or a combination. Most people are not familiar with reading canine body language and training. Because of this, I recommend to work with a professional trainer. Researching on your own will also be helpful. Familiarizing yourself with canine body language and dog training can help you to recognize what your pet is trying to say. You can find many books written on the topic and there is a trainer named Victoria Stilwell who I think is particularly helpful. Best of luck.

I recommend that you keep them separate until you are sure they can get along when you are gone. Separating by a baby gate or keeping them on leashes would be fine. If they fight over toys, then all toys should be removed from the area. You also. Red to keep a close eye on them around feeding time. Here is a helpful article https://www.animalhumanesociety.org/behavior/how-introduce-dogs

Female to female aggression is very hard to manage. Are all your pets spayed and neutered? This is the first thing I would do if not. Some of the worst injuries I have seen are between two females in the same household. They are likely establishing dominance and there are things you can do to reinforce the “leader” by feeding them first (or feed them all separately), letting the alpha dog walk in front when taking walks. I strongly suggest you work with a behaviorist and take aggression seriously bc I have seen it escalate quickly. Hope that helps.

If there is a neutral place in the house that way there is no territory problems it would be best. You can keep them both on leashes to control the situation. make sure all food and beddings are separate also. Once they get used to living together and no one fees jealous then they will be fine

You will likely need to separate the new dog from the 2 "older" dogs for a period of time. Spend time with each separately, but make sure that they cannot see the new dog, i.e. keep him in a separate part of the house behind a closed door for at least one to two weeks. Then you can allow them to see each other, but not have contact. Move slowly, from this phase on to allowing them to see and smell each other across a barrier such as a baby gate. Finally, allow them to spend supervised time together. Reward good behavior with high value food treats (i.e. bits of cooked chicken) and go slow.