
If she's fine for weeks then possibly it is a niggling issue(s) building up to breaking point - in that situation the fight then breaks the tension and it starts all over again. With one of mine the stress built up that way until she was unable to cope, got very ill for a week then recovered (the cause of stress in her case being the owners' handling and training methods, so the week of illness gave her a break from that and the stress levels dropped back down again), then the cycle started over.
It's always worth asking behaviourists what they charge, whether they'd do instalments etc - we all work differently. Some charge hundreds, I charge very little (too little really!) but rather than do one visit and a report then phone/email followup support, I like to do the assessment then follow-up visits to make sure things are on track. So I charge small amounts at a time, which many people find more manageable.
> although any decent behaviourist will also be a good trainer.
This. The two are inseperable in my mind but in this situation, you must get a behaviourist to be sure you're getting the scope of knowledge required. Definitely check insurance if you have it, many will cover behavioural consults.
In the meantime, what do you feed them? This can make a big difference. And one training tip I will give - reward anything and everything that is NOT aggression/tension in any form. So if he walks by and she does nothing (and I mean nothing - no stiffness, staring, whites of the eyes, licking lips, deliberately ignoring him), praise and reward. If you can see her starting to get tense because he's doing something, move him away or if she's put herself in a position she's not comfortable with, encourage her to move (or again, move him if that will calm things down the safest way). Keep a diary too - record anything that happens to either dog, any bad interactions with other dogs/people/kids, anything that frightens them etc as all of those things can have an effect at home. And at home - body language, presence of food/toys/you, anything really. You might be able to identify triggers that way, then you can manage them.
I would also start to get yourself familiar with calming signals and stressful body language - plenty of info out there on the net, videos on youtube etc. The better you can read your dogs, the more you will be able to see potential situations beginning and diffuse them long before anything actually happens. Prevention is better than cure as they say, and nowhere is that more true than when dealing with aggression in dogs.
Incidentally - how thorough was the vet? I have known many give a dog a once-over and declare them fit and it is not enough. A proper physical exam with manipulation of joints and comprehensive blood tests including thyroid is what's needed. So much can be missed otherwise, as my own dogs have shown me numerous times - in particular my first rescue dog was diagnosed with a touch of arthritis in one hip, when in reality her whole pelvis was tilted and twisted and she had several misaligned vetebrae, all of which made her aggression much worse. And one of my others started snapping at dogs - totally unheard of for her, she's the best dog I have for teaching others and NEVER snaps - the vet missed it completely but by chance, when she went on painkillers for something else some time after the snapping started, we found she had low-level pain which I now know is arthritis.