If/when you go for a referral, please do not let them vaccinate your dog. With the limp, and the eye, your dog may have a central nervous system infection, or who knows what, aand only healthy dogs should be vaccinated.
I had a head injury once and had that "one pupil larger" thing for awhile - I used massage and chiropractic care.
If this were my dog, I would want a full blood test (including thyroid) and run a tick test, unless your dog has lived it's life in a conrete city. My next step would be a K9 chiropractor.
That one eye thing *may* be more of a neurological condition than an eye doctor, I am not sure, but that's who they sent me to. I have found that most neuros are pretty limited, and their tools are very expensive (Mri's and ct scans).
It's really nice if you can find a vet that I a good problem solver with an open mind, and, as marko said, it takes awhile to find that and build that relationship. Having had senior dogs and been out on a limb not having a regular vet at the time (mine was in the proces of retiring), it's an awfully hard position to be in.
I wish you luck with this - it sure would help if these dogs could talk and tell us what they might be thinking.