When you put two dogs of the same sex together in your home, there is always a risk that they will not be able to get along. Sometimes they will fight, and it can be severe. It's important to realize this is usually not a temperament problem with either of the dogs. This is nature taking its course. Dogs are much more the victims of their own instincts than humans are. Human siblings, you can reason with (sometimes), and they can learn that they have to get along. Dogs are not capable of that kind of reasoning. They will largely do what their instincts drive them to do.
You can go a long way toward solving the problem if you first realize and accept that fact.
Second, you should never, ever put two dogs in a position of having to compete for food. That includes their meals, their treats, toys that are edible, and any toy they jealously guard (to the dogs, apparently a lot of non-edible toys still have food "value," judging from how they behave). Remove all those items whenever you are going to have the dogs together. When you are going to give them any of those things, physically separate them. Don't expect them to share these things. They were not wired to do that. Dogs will fight over food and edible toys who would never fight over anything else.
Jealousy isn't really a very useful word when it comes to dogs. They need to know that there is plenty of everything they need for the number of dogs using those resources. Otherwise, in nature, they would drive some dogs away to form a new pack. But they can't do that in your home.
So, for example, any toys they don't fight over, you need to have plenty of those toys if you're going to be able to safely leave them available to the dogs when they are together.
Your attention is an important resource, too. Each dog needs time with you every day away from the other dog. Even dogs who fight at times can be extremely dependent on each other, and they must learn to tolerate being separated. They must learn. This is very important. You don't do dogs any favors by letting them get that dependent on each other. It is very unhealthy for them. At first you may need to have someone keep the other dog entertained while you work with one of them, but they will quickly become accustomed to the routine.
At this point, that individual time with each dog needs to be training time. I highly recommend the book Dog Training for Dummies by Jack and Wendy Volhard. Start immediately with each dog on the leadership exercises: the long down and the long sit. You need the instructions to do these exercises, because they are probably not what you would guess they are! If it's more available when you look for the book, the Volhard book The Canine Good Citizen also has this program in it.
Do the rest of the basic exercises in the book, too--with each dog, away from the other dog. Each dog needs a strong individual relationship with you, and training is the humane way to do that. The Alpha stuff, well, I don't place a lot of faith in it. We are often wrong about which dog is alpha, for one thing! If you teach each dog to obey you, you call the shots with them, and you give each dog an equal amount of individual time, you're likely to do much better than with the alpha "tricks." I actually found when I had a strong pack leader dog who tended to be aggressive about food with other dogs if he had a chance, that it was far better to feed him LAST. He was then reminded multiple times a day that he was not in charge of feeding--I was!
Outings are important in bonding with dogs. Obedience class is a great way to do that, and also provide some of the individual time with each dog. I know it's twice as much work to take each dog to class separately, take each dog out to practice separately, and make that conscious effort to spend individual time with each dog all the time. Eventually it won't have to be every day, but I would keep it to at least three times a week for awhile, and never drop below once a week. You'll find a lot of other rewards in doing this, besides hopefully stabilizing the two same sex dogs into a peaceful lifestyle.
Even if you do achieve harmony between the two same sex dogs, you will have to be extremely cautious about adding more dogs in the future. Every addition to the pack can cause fighting to start again. When dogs fight to the point of injuring each other, they can't be kept together. Then you wind up with a more complicated lifestyle, keeping your dogs separated all the time. It is done every day by many people, but it's a big change for the whole family.
When you lose one of the dogs of the same sex, and are looking to get another dog to live with the remaining dog, I strongly recommend you get a dog of the opposite sex. Dogs of opposite sex get along so much more smoothly and safely than same-sex dogs. However--still don't give them food, treats, or edible toys when they are together. That is never safe, no matter what the combination of dogs. It may go along for awhile and seem to be okay, but it's a time bomb.
Usually, removing the food from the situation and instituting the training and the regular individual time with each dog will save the situation. If you have further fighting, it's time to call in a behavior specialist to come to the house and evaluate the situation. Sometimes you can let them fight it out, but that is dangerous, and you need an expert in person to assess risks.
It's also important to consider the living situation. For instance, do you have a fenced yard? If you do, be aware that dogs can "run off" a lot of their differences. When you arrive home from work, or come back from an outing with one of the dogs (and all the other times that they tend to get testy), if you have a fenced yard, give them supervised running time together out there. When you're playing with them, don't throw a ball in such a way that they'll compete for it. Have two balls, and throw them two different directions. Until the dogs can each play with their own ball and not jump the other dog, don't even play ball with them together. Do it when you're working with them individually.
There are some really tragic situations where dogs will rip each other to pieces--even resulting in the death of one of them at times. This is caused by instincts. Nature wants dogs to spread out and have a leader in each small group who can guide and protect the pack. When two same-sex dogs are not able to work out which of them is leader, sometimes your only choice is to separate them. It is cruel to keep two dogs together that fight to the point of injury, even when they seem to love each other. This would not happen in nature. One would leave and form a new pack. It's a problem we create by how we keep dogs in our homes--the combination of dogs we put together, and how we manage them.
How to Help Same-Sex Dogs Get Along in Your Home
I'm not optimistic about these situations once the dogs start getting injured. At that point, separation is usually best. Some owners choose a lifestyle of keeping the dogs permanently apart in the same home. Other owners, who either don't wish to adopt this lifestyle or perhaps have household situations that could result in the dogs being put together accidently, may instead choose to rehome the younger dog.
If you haven't had injuries, here are some things that can help:
1) Spay/neuter both of them.
2) Work with your veterinarian to be fully aware of the medical issues affecting each dog. For example, a dog with hip dysplasia, a damaged knee ligament, deafness or blindness will react differently to other dogs. A seizure disorder could make one dog the target of another, or could cause the dog in the seizure to become aggressive. Some medical disorders will call for separating the dogs at least part of the time.
3) Give no food of any kind to them without enforcing complete separation until both are finished eating. Any toys they would fight over need to be removed, and given only when they are apart. Same for chew items.
4) Obedience training. You need to be able to control EACH dog without your hands or a leash, just your voice. Then you have a chance of controlling both when they are together. You do not want to be sticking your hands between two sets of flashing dog teeth.
5) Take each dog away from the house daily for training time away from the other dog. This strengthens your individual control over each dog incredibly.
6) Comb out or in some other way thoroughly groom each dog daily. This makes it a lot safer to put your hands on them when they are aroused, plus it powerfully strengthens both their individual attachments to you and their obedience to you.
7) Have them do a 2-minute Sit-Stay and a 4-minute Down-Stay about 4 feet apart, every day.
8) As long as you have concerns they might fight, separate them when you are not able to supervise them.
9) A fenced back yard is a huge help with this. When you arrive home, immediately let them out to run together. They will argue a lot less if they can solve some of their relationship issues through running together. This is particularly important when returning with one of them who has been out with you. If they are cooped up in a small space when feeling this way, fighting is more likely.
10) Be careful about when and how you intervene. An owner interrupting the interaction between two dogs at the wrong time can actually trigger fighting. Dogs are also capable of fighting to get your attention.
At some point, the dogs often have to be permanently separated rather than keeping together two dogs who fight. Be alert, too, to the problem of this relationship pushing one of the dogs to become dominant to an unhealthy degree and the other to become submissive to a point that's not good for her, either. Dogs who have been in a relationship with another dog of the same sex that turned into fighting are then not good risks to live with another same-sex dog in the future. This is a stressful relationship for the dogs as well as for the human family members.