Welcome to JustAnswer, and I'm sorry to hear you are having such a hard time with this. Your mother's symptoms suggest there is alot going one here, and probably more than one system is affected. She likely has renal problems, and may have cardiac problems as well. She could have a chronic renal insufficiency, or even SIADH, which essentially exhibits with symptoms of hyponatremia.
Here's a link to SIADH. This link is from the UK, but I just like the format. Anyway, as you can see when you read this information, there can be many causes for this. Although, in most the patients I have worked with, the syndrome was idiopathic.
At any rate, my main point here is that it is inexcusable for her doctor to "just decide" that she doen't need a referral to a specialist, since he hasn't come up with an answer. You are right to be concerned. Unfortunately in my years of experience with our Elders, this is way too common. Some doctors "just decide" that elders are not worth the effort. In this case it looks like he is guessing about what's wrong, and just doing a trial and error type of approach. Fine for cars, not so good with people, especially elders.
My suggestions to you:
Set up an appointment just to discuss your concerns with this physician. Let him know you want him to be more proactive. Many times the "squeaky wheel" provided by a concerned family member can get alot of "grease" so to speak.
If you have already done this, seek out a second opinion. This is easier said than done many times, since the second opinion often will be provided by a doctor you are referred to by your own doctor, who will then agree with the original decision.
If your mother's doctor is in a "clinic" type setting that has a separate staff of administration---complain to the administration. This usually gets some action.
If you don't get action soon, the best thing to do is to change doctors. This is too important to mess around with.
I'm really sorry your mother is having such a hard time with her doctor. This is just pathetic. She really does need a referral to a cardiologist and/or a nephrologist. I wish you well, and good luck to you and your mother. I really wish I could do more for you.