My experience along the line of your question was I asked my primary care what was a good exercise/running HR for me. I asked as I was inclined to run a bit higher than the general rule guideline.
He referred me to a cardiologist for a stress test. That came back to him and was the first indication I had some heart problems...maybe blockage, which I did not. My primary care discussed with me and I decided to do nothing. Months later when I said I feel some irregular heart beats he referred me to a cardiologist. From that time on all my medical attention for my heart has been provided by a cardiologist. I do not discuss my heart condition with my primary care, other than as a reference when I get my annual general physical.
Long story, but it contains a recommendation: see a cardiologist.
i wouldn't trust a family doctor to switch from one kind of meds to another though.
for example: from betablockers to calciumblockers
did the family doctor diagnose it as SVT? if so go to cardiologist.
if cardiologist has diagnosed the SVT and your symptoms are due to meds,
then i guess the family doctor is fit enough to experiment with lowering/highering dosage or switching to a different betablocker.
what exactly are the symptoms that are bothering you?
I'd seen a cardiologist if I were you.
It all depends on the doctor's knowledge in cardiology topics. Some doctors cannot even interpret an EKG, except saying the rhythm is normal or abnormal.
Remember, SVT is not life threathening but annoying, and cureable. A cardiologist can probably give better advice on how to cure it, and if not, which medications you need to control it.