Generally, corticosteroids such as prednisone are tapered off based on how long it has been given for, what the condition is and if there are any other underlying issues that affect this.  However starting with a high dose, then going to a low dose, then high again could mean that it was the higher dose of steroids that was working, it was reduced to see if it would still be effective at the lower dose, then increased again since the lower dose was not being effective.

If this is the case, then it is important to have a veterinarian that knows the condition and is monitoring your dog based on the condition while it is being tapered off. You can inadvertently cause issues such as iatrogenic Addison’s disease if you discontinue prednisone too abruptly.  (Here’s an article on Addison’s with a brief section on iatrogenic Addison’s disease:  https://vcahospitals.com/know-your-pet/addisons-disease-in-dogs-overview)

With all this in mind, I would strongly recommend you find a veterinarian that will support you through weaning your dog off steroids and trying alternative therapy if you do not agree with the protocol you are currently trying.