> She have seen the vets and does have a mild case of Hip Dysplacia but it does not effect her at all,
Are you sure? I have seen dogs with barely detectable HD suffer disproportionately huge amounts of pain with it and one of those would try and attack any dog that happened to touch his back end.
Presumably there was a reason her hips were x-rayed - does she show signs of pain around her back end with manipulation? I ask because some issues do not show on x-ray and MRI may be a useful tool, despite what's been said.
One of mine went in for a checkup after she refused to do some contact obstacles at agility, no other signs, and the vet found slight pain - x-ray showed mild HD in one hip. She had 4 months of hydro and made no improvement so she went back to the vet, and some back pain was found. I pushed for MRI, and it turned out she had a chronic prolapsed disc which had been there for years. She was actually in quite a bit of pain but to the untrained eye, it was anything but obvious. When she is sore she can also be very reactive to other dogs because of it. It's a self-fulfilling prophecy with her - she worries that they will hurt her, so she tenses up, which aggravates the problem (pressure from the disc on her nerve roots causing back pain, muscle spasms and sciatica), which causes her pain which is then associated with those dogs.
Or from another angle, unprovoked aggression can be a sign of not only neurological problems, but hormonal and in particular, thyroid trouble - for that you would need to run a full panel (free T4, free T3, total T4, total T3, TgAA antibodies). Anything less is not worth the money for diagnosis in a case like this.
On your family situation - I would not take her round their houses at all, I'm afraid. Aggression is rooted in fear, and if she is as aggressive as you state then every time she's near another dog, it is intensely stressful and frightening for her. So taking her there is only making it worse as it is too much for her and potentially, it will be driving a wedge between you and your family as well. Rehabilitating an aggressive dog is very wearing at times, you need all the support you can get.
What I would do at this stage is get her to a vet behaviourist, not another "normal" one. Lincoln vet uni has an excellent behavioural centre, and I believe Liverpool teaching hospital has one of Lincoln's people now too. They will pick up on everything and if necessary, will also be able to advise you on behavioural medication with full knowledge - again if she is as aggressive as you say, she may need that extra help, especially with the lack of success in training so far.
What have you actually done with the trainers/behaviourists you've seen?