How to get my dog to accept a new dog in our home without fighting?

You're right that there can sometimes be problems when introducing two dogs for the first time, especially if either of them has any history of aggression towards other dogs. I would recommend introducing them in a neutral place at first, like a park. Keep both dogs on leash, let them sniff each other briefly, then go for a walk together. This allows the dogs to get used to each other's presence without feeling pressured to interact. After the walk, take them both home and into the house together and if things are going well, let them off-leash to relax. If things don't go smoothly, it would be best to get help from a veterinary behaviorist (ideally) or a good reward-based trainer who can work with you in person. You can search for a behaviorist in your area here: www.dacvb.org or a qualified trainer here: www.ccpdt.org.

Your house is a lot different, and your own dog may be feeling like there is a bit of an "intruder" situation going on. it may take some time for your dogs to all get along, especially if the change was recent. Until they get along better, the dogs should only be together when able to be supervised by you. You may also want to pick up items of contention such as beds, toys, treats, etc that may be fought over if your dogs feel threatened. If a fight breaks out, immediately separate the dogs for a "time out"/cooldown, and then reintroduce when all dogs are calm and relaxed. When you are not at home, the dogs should be separated or crated in separate crates to avoid a potential fight. If the issue persists, speaking with a trainer or behaviorist may also help as they can often observe what is going on in the home, and can make suggestions based on your specific needs.

Outside is neutral territory; inside is your previous dog's territory. There isn't much other than allowing him time to get used to having a new roommate. Try to keep things as normal as possible. Continue the walks outside so they can bond. You can also use Adaptil diffusers or DAP collars to provide calming pheromones.

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

Always introduce dogs in neutral territory. So, not on the property at all. Somewhere like a local park so they can meet each other without anyone being territorial. Do this a few times before moving in. Keep both dogs on leashes so you have control over them if things go awry. If the dogs are not spayed/neutered that should be done because raging hormones often causes fights especially when females are in heat. I would also suggest start using Adaptil diffusers (calming dog pheromones) in the house starting a couple days prior to moving and refill them every 30 days for the first couple months. I would also get Adaptil collars for both dogs to wear starting a few days prior to the first meeting. These particular calming chews (Solliquin) also help quite a bit. https://worldtails.securevetsource.com/site/view/198944_HomeDelivery.pml?s=adaptil&hierarchy=&sort=score%20desc https://worldtails.securevetsource.com/itemView/view/198944_HomeDelivery.pml?productId=117298

I'm sorry to hear that things aren't going well with your new dog. Unfortunately, it sounds like this may not be a good match - just like humans, some dogs have very different personalities and may simply not get along. If you want to try keeping both dogs, I would really recommend getting in touch with a veterinary behaviorist who can evaluate the dogs in person to give you a better idea of whether this is a fixable issue - if so, he/she can help you put together a detailed step-by-step plan to work on the problem. You can search for a behaviorist in your area here: www.dacvb.org In the meantime, I would recommend keeping your older dog on a leash or physically separated from the other dog with a baby gate or other barrier. This will allow the younger dog to relax a bit without being harassed. If things go well like this for a few days, you can gradually allow short periods of contact between them. Reward both dogs when they are together, and particularly praise and reward your older dog for calm behavior around the new dog. You may also want to try a DAP pheromone collar on both dogs, along with a natural calming supplement such as Zylkene or Composure for your older dog to see if this helps a bit.

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!