Owners know their pets best. If you are concerned about her breathing, I believe further diagnostics should be done for her heart and lungs (both heart and lungs because the heart can so easily affect the lungs). She needs further diagnostics because I don't think you will get your answer for what is going on with her without having more done. By further diagnostics, I mean the following:
1) 3-view chest radiographs: this means that one x-ray is taken of her chest with her in each of three positions: laying on right side, on her back, and on her left side. This is the only way to 100% thoroughly evaluate a dog's chest. Many vets (myself included) are limited in how much they can do because the client can only afford so much, and x-rays are expensive. So often we are limited to being only able to take 2 xrays of the chest (one from the side, the other with the dog laying on his or her back). But the absolute best is to take all three views, when financially possible. The reasoning for this is that when you are looking for very important and subtle changes to check for any type of disease, there are areas of the lungs and heart that are best evaluated with each view. Taking only one or two views leaves some areas unevaluated, therefore the possibility still exists in those areas that there is disease going on that you miss.
X-rays are used to evaluate heart size and shape, the size and shape of the heart and lung vessels, the bronchi and bronchioles in the lungs, and the surrounding lung tissue. We use them to check for diseases such as cardiomyopathy (problem with the heart muscle, which usually shows up as the heart being too big), valve problems in the heart (also shows up as enlargement in certain areas of the heart), thickening of the bronchi or bronchioles (which could indicate some type of obstructive pulmonary disease or allergy), tumors (hate to mention this but must be on the list), fungal or bacterial pneumonias, fluid in the lungs, or problems with the trachea (breathing tube). All of the things I just listed can cause labored breathing.
2) ECG and/or ultrasound of the heart: If there were to be any abnormalities found on the xray concerning her heart, the next step would be to perform an ECG on her heart to make sure it is functioning correctly. An ECG is a printout of the electrical nervous activity going through the heart that keeps it beating. There is a very specific and repetitious way that the nerve signal flows through the heart to keep it beating, and any changes in this will show up on the printout and can be evaluated. Certain types of changes can pinpoint specific problems with the heart, for example, a wide QRS complex (the waves on the printout) can indicate that the heart is too large.
An ultrasound of the heart should be the next step if the ECG is abnormal. An ultrasound of the heart is just like ultrasound of anything else, it will show it real-time on a screen as it beats. The key to this, though, is that an *experienced* cardiologist is the best person to evaluate a dog's cardiac ultrasound because of how complicated it can be to make sure that you are viewing the correct spot on the heart with the ultrasound probe.
3) Abdominal x-rays would be a good idea, too, because sometimes heavy breathing can be due to something in the abdomen pressing on the lungs. For example, an enlarged liver, or fluid in the abdomen, can press on the lungs and make breathing more difficult. One or two views of the abdomen is sufficient to evaluate this.
4) Complete bloodwork (including a heartworm test) is never a bad idea. This is another way to evaluate most of the body's functions and can give more clues as to what is going on. I know you said that Becky is on heartworm prevention. I would still very strongly recommend that she be tested for heartworms (unless she has been tested in the past 6 months) because it is very easy to test for and can cause the exact symptoms you describe.
If your current vet will not do any more for Becky, you should consider finding another vet who is willing to address her breathing problem. Please re-read this answer again, and think of any and all questions you may have. You can always ask me more by replying to this answer. I am sure you will have more questions, because I know this was a lot of information. And I may not have answered your question thoroughly. If not, please let me know. I will help you until you are completely satisfied.