I am sorry to hear about you experience with your veterinarian. I too have noticed how very expensive foods are often promoted despite other more affordable brands being available.
There are a number of possible causes for the itching that you described, food allergies are a possible cause but often they are less likely to be the culprit. The most common causes for itching are flea bite dermatitis, and fungal or mite infections. The reason why I mention this is that it is more important to diagnose/treat the more common problems that exist before you spend money on buying new foods. As flea allergy is the most common problem that causes itching, and all it takes is a flea bite to set it up (which may happen outside and you may not see) it is important that you give all animals in the household a monthly flea control. An effective flea control is Advantage - you can even buy this on Amazon, it is sold based on weight. Don't waste your money on flea shampoos or sprays, they don't work.
As for testing for skin infections - that is something that you would need to have a local vet do, usually a skin scrape and fungal culture. Also once a pet is so itchy and causing damage to the skin they may often need medications to reduce the itching or antibiotics, shampoo. Even if it is a food allergy sometimes they will not respond well without they use of other medications.
Ok now about the food, just a reminder I would not even consider switching the food until you try some flea control as food allergies may not even be the cause. But about good foods....Alpo is not as good quality as some. I really like the Nutro brand, it is a good food and not very expensive. You should be able to find it at most pet stores e.g. Petsmart.
When a dog has a food allergy it is usually in response to the protein in the food, for example a lot of dogs have allergies to chicken, beef and lamb so the best step when choosing a food is to pick a novel protein such as duck, salmon, venison etc. These foods may be labelled as "limited ingredient diets or LID" Make sure the food or treats do not contain any chicken, beef or lamb, unfortunately you should not continue to use the dog bones.
There have been no scientific studies that show that grain causes any allergies in dogs so I would disregard all of the hype around "grain free" diets. Ultimately it is ok if the food you choose is grain free, for example I think the Nutro salmon, duck is also grain free. Just don't buy a food because it says "grain free".
So to wrap up...you should make sure the dogs are on flea control and then choose a food that is based on a novel protein - look for salmon, duck, venison and rabbit on the label. Make sure not to feed chicken beef or lamb. If you do decide to start the dogs on a food trial for allergies make sure to switch the food slowly by intitially mixing the foods together then weaning the old one out. Then feed only the new food (no treats, unless they are hypoallergenic i.e. no allergenic proteins) for at least 3 months, you will need this much time to see if the dogs respond.
Please let me know if you have any follow up questions. I wish you the best of luck.