Although neutering male dogs can sometimes help prevent fighting, spaying females seldom has the same effect. Your problem is far from hopeless, though, and giving up one of the dogs doesn't have to be an option. Dogs were designed by nature to run in packs with a clearly defined order of authority from the top dog on down. As long as everyone knows his or her place and follows orders, life is usually peaceful. With most dog packs, it's easy to see who's boss and how the rest of the dogs fit within the order.
Some dogs are born leaders, others fall into the alpha role because no one else wants the job.
Most dogs don't mind holding a subordinate position and seldom challenge the alpha dog's authority. The alpha makes and enforces the rules. Alpha dogs enforce their authority by the use of stern eye contact, growling, dominant body postures and if that fails, biting and fighting. If you watch your dogs closely, you'll see examples of this eye contact and posture in their daily activities. You are alpha in this pack.