diagnosis or treatment for my 15 year old with tachycardia.

There are two scenarios and time correlations that link tachycardia and low blood pressure. If the blood pressure drops first such as in orthostatic hypotension/POTS ( when you first get up from sitting or lying down) the heart rate increases to compensate for the low blood pressure to prevent passing out. If the heart rate increases first and gets so fast (> 180), the heart cannot fill with blood sufficiently between beats and the blood pressure drops as a result of low cardiac output. In The second situation, keeping the heart rate from escalating so high will prevent the drop in blood pressure and a medication like a beta blocker can be safe and useful. it would be good to know what her resting heart rate is when she is not in tachycardia. If it’s 65 to 70 or above, a dose appropriate beta blocker may be very helpful in controlling her symptoms until the cause of this is determined. Regardless of her cardiologist reputation, I think a second cardiologist’s opinion ASAP is warranted.

I started having heart rhythm problems at age 14 for 7 years. Never went to doctor but read from a doctor column in news that some people are extremely sensitive to caffeine. Is she drinking colas, Mountain Dew, coffee, energy drinks, eating chocolate?

her heart rate at rest varies but is usually in the low 80's
the heart monitor she wore for ten days shows her heart rate slows way down when she sleeps and sometimes drops into the mid 50's. We were told this is normal

she does not drink sodas or energy drinks. She doesn't like anything carbonated so we have not had to worry about the caffeine. She eats chocolate but not excessive. We don't keep a lot of it in the house.

From what we have seen her heart rate gets high and then the blood pressure drops. They ruled out POTS due to this not occurring when there is a sudden change in movement. The heart rate rises simply with any physical activity, regardless of how extensive it is.

IT might be Vagus nerve intonality. The Vagus nerve is part of the parasympathetic nervous system, the 'side' of the body's nerve supply that is meant to regulate and to calm. The sympathetic nervous system is the 'arousal' mechanism that is part of the 'fight or flight' response to stress. The Vagus nerve runs from the brain all the way down to the lower gut with at least 50 branches off it, running to most organs and into tissue. You might wish to research 'Vagus nerve tone' and cardiac reactivity and arrhythmias. Here's a fr'instance:
https://www.nature.com/articles/s41569-019-0221-2
The medical community feels that any HR between 60 and 99, inclusive, is 'normal sinus rhythm'. Some cardiologists have begun to question those range limits, especially the lower one, and think that 50 is more reasonable. The upper one, believe it or not, is pretty robustly supported. It seems high to me, but...your daughter's resting rate is well below that threshold.

I wonder if any of the knowledgeable people here know whether avoiding activities that raise the heart rate for some period of time could somehow heal whatever is going on. I know this is vague!

Does walking raise the heart rate? Are there certain activities that don't, like, say, swimming? Can the heart be retrained?

My kid has a resting heart rate of 140 at one point, as I wrote, and my son's heart rate went really high after any exercise- at age 10 or so. Somehow both resolved and I have no idea why. Kid with high resting heart rate had a positive Lyme test and was eventually diagnosed with lupus, has type 1 diabetes. Co-morbidities can be important but so far your daughter doesn't have any!

Did your cardiologist suggest techniques to helplower your daughter’s rapid heart beats? I occasionally have intermittent tachycardia which can be helped with slow, deep measured breathing. Here is a Mayo Clinic article about Tachycardia:
https://www.mayoclinic.org/diseases-conditions/tachycardia/diagnosis-treatment/drc-20355133

Here is an article by Mayo Clinic about lowering your rapid heart beat with measured breathing:
https://www.mayoclinic.org/diseases-conditions/tachycardia/diagnosis-treatment/drc-20355133

I wonder if this is some form of dysautonomia. There are dysautonomia clinics in some hospital systems. I just randomly ran into this on Facebook https://www.facebook.com/groups/1016433459359125/?hoisted_section_header_type=recently_seen&multi_permalinks=1285375155798286

Apparently people are using a vagus nerve stimulator. I know nothing about this and did not investigate so just passing it along. Functional medicine might be helpful alongside cardiology.