I haven't been on for a while, but have posted about this before.
In the middle of last year, two of our bitches, Mother and Daughter, now aged 6 and 3, had a couple of fights. The second caused minor damage, one bitch requiring stitches to her leg (although I am pretty sure they didn't fully intend to seriously damage each other) the other antibiotics for puncture wounds below her ear.
We have since kept them living apart, one with our other bitch and one with our rescue dog, although they have had sight of each other through a stairgate and we started walking them together. During the walks when we have had the two bitches alone out together they have been off lead/playing with a ball and all has been fine. I have also walked all three bitches together on lead a few times and although I have been wary and therefore kept them under strict control (must walk to heel, paying attention tome, not anything else) they have also been fine on these occasions.
As they have seemed to be getting along better and I had hoped the walks would encourage them to have positive associations with each other, I tried them together again today in the garden, the result was a fight after a couple of minutes. It was very stupid of me and fortunately neither was hurt.
We did get a behaviourist out when the second fight happened, but he was useless if I am honest and there isn't much choice of behaviourists where we live. We are moving to the outskirts of a city next year and hoping to find a better behaviourist then. However, I wonder if I am just going to have to accept that these two girls will never get on with each other? Both are very well socialised and excellent with other dogs, even those not well socialised, the problem is purely with each other. Keeping them seperate is a little awkward, but doable and both bitches seem happy, as do our other dogs.
Does anyone have any experience of this sort of thing or advice to offer please?

I had 2 boys the same age, both got on fine for 3.5 years until I added a bitch, then one weekend hubby took one male on holiday and I stayed home with the other & the puppy because we had a show, and when hubby came back the 2 boys just went for each other. Some stupid moron 'behavourist' advised us to muzzle them and let them fight it out, we did this not knowing any better and they fought to exhaustion, a horrible sight. Of course after that they could not be in the same room as each other, luckily they were both small breeds and were fine seeing each other through a stairgate or we would have had to rehome. Occasionally we did have them out or walked them together, but I was always watching like a hawk. 5 years later we moved house and hubby for some reason started having them out together more often and they seemed to have settled down, I never left them alone together but regained the confidence to walk all three by myself, and things seemed much improved until sadly one died last summer. If your two girls are happy as they are and you are certain you can manage the situation (no small children or careless OHs to leave the gates open) it's not necessary to rehome, but it is harder to manage dogs in separate groups like that of course.
Are either of the bitches spayed? Sometimes this can help to reinforce pack order. If one of them is more submissive then I suggest spaying her might help. We had 2 half sisters, similar in age who would fight at 'hormonal' times. One is now spayed and she is a lot more chilled and doesn't react when the other bitch takes offence at something.
Also, be very aware of your own behaviour and what triggers fights. With ours it was always something that we did (often sub consciously) that triggered something. They would never fight when we were not around. Avoid the opportunity to squabble over high value items. Our high value item was nearly always our attention. If one was getting attention and the other seemed to be getting her back up, we would just leave the situation, walk away and neither got any attention. Seemed to diffuse the situation right away.
It's not that our fights were just handbags or anything either...they would have killed each other is we hadn't got them apart - of that i am certain.
Once you have seperated for any length of time I think it becomes increasingly difficult to get back together. We would only seperate for a couple of minutes then get them back together, not forced, but just leave the gate open and walk away. Not make a fuss, just let them mingle in thier own time and space. Anything forced or pressured and the tension rises and 'bang' we're off again!
This is how it worked for us but I know other situations are very different and triggers vary so much. Sometimes the fall out is just going to be permanent and a seperate pack is the only way forward.
Good luck
> Also, be very aware of your own behaviour and what triggers fights
I totally agree with this. My girls are the same ages and relationship as yours. Mum is 6 and spayed and daughter 3 not spayed. They have mild squabbles when the younger bitch is hormonal, as just now, two months after her season she is having a mild phantom. No hoarding of toys, or milk production as her mum used to have but totally obsessed with me, wanting to be close. Licking me all the time, if I let her. Obviously discouraging the behaviour. I made a massive stupid mistake the other night though. The girls sleep in their own beds at the side of my bed. Mum always in the bed closest to me and daughter the next one along. They rush upstairs at bedtime, take their places and wait for their "going to bed" treat. The younger girl had taken mum's bed. Mum looked "upset" (non aggressive) and I told daughter to "get in her own bed". How stupid can you get. I helped her along and mum took her place in her own bed. Daughter then attacked mum and I had to drag them off each other. Obviously, If I had left them to sort it themselves, this wouldnt have happened. You have to be so careful. The only other time this has happened has been when one has been guarding a treat. Something I never allow now. Trouble is, I dont know how far they would go as I have dragged them off each other each time. The last time, daughter had a mouthfull of mum's long coat so there must have been some grabbing involved. Other times, they are inseparable. Constantly grooming each other etc. Its a difficult one.