Your gut instincts are correct with regard to the expectation that vet records can be shared. I've got multiple pets,and multiple vets--; my regular vet,--she works specific hours and is close by--, a vet that does "routine" check ups (as he's cheapest and close), and then my "main vet"--the one I know I can call in an emergency and whom I'll drive across the city to see when the chips-are-down. In all cases where, after consulting my first vet and finding she wasn't able to provide the indepth care we needed, the records and/or tests we took at the onset would go with me to my back-up main vet.
I don't understand why the vets you're dealing with are trying to pick your pocket further by suggesting you redo tests --(some bloodwork would be necessary though, to keep an eye on the levels that would indicate immediate emergency) when they've got the basics right there-- if they're talking surgery, why even more tests?-- Just dive in and explore while they're there, I mean, if they're convinced surgery is needful, why more diagnostics?--what do they need to see further that they could see during surgery?... It seems like the typical gimick many vets do-- especially during an emergency when they know the owner is in a most vulnerable state.
I'd be curious to know if there's a governing, oversight body --like a veterinarian association to which the vets you're dealing with would have to answer to. I'd push further to find out why they're saying it all has to be done again.... Thing of it is.. is that whomever it is, vets are in it to make money-- it is why they have the business, so do expect to pay something.
As Julie, another poster, rightly points out-- this is a matter of you and your dog--and what you know you can live with--- what your finances are and how much you're willing to spend on a dog that's entering it's twilight years, now with liver complications that can be expensive, -- you need not only non-greedy vets, but one who will lay it all out for you-- and not take your money knowing full well you beloved pooch realistically only has less than a year to live, for example. Knowing what the odds are in tandem with what you know you can handle-- and listen, sometimes saying good bye IS the right and loving thing to do-- we have to ask ourselves, when faced with these kinds of delimas-- are we keeping our four-legged family member around for its sake-- and what's his/her quality of life going to be during this time--- or are we keeping them around for our own sake, because we can't bear to part with them? ...
I've been in your shoes four times now in the last eight years, during which only once was the decision was taken from me as Kiara passed on whille in hospital on her own while at the vets, but the other three I knew they'd had a good life but that they'd reached that stage that for me to pour money into them when in reality they had less than 20% of their true, healthy, happy selves---it wasn't fair to keep them around--- I had to be realistic and look at the whole picture, --and each time it was a heart-wrenching, mind-numbing and excruciating decision, --no other decision I've had to make in life compares to this kind.
I hope you find a vet that will provide an honest, overall, weigh-the-odds diagnosis--and one who won't run unnecessary tests simply because he/she has an affiliation with the test-lab! I hope once you get your answer, you can either afford what it'll take to make your pooch comfortable in the face of what's going on in his body-- or that you find the strength to make a painful decision.
I wish you and your sweet baby all the best--
25 years of dog/cat ownership; previous vet assitant, current Mom to a brood of ten--and part time dog trainer.