If you have been using the spray for a week, it doesn't sound like it is solving the problem. The antibiotic and steroid spray is a treatment for skin infections and irritation. It is a good treatment for hotspots.
What does the lesion look like (bump, with or without hair, ulcerated)? How big it it? Where is it?
To get an accurate diagnosis of skin lesions, a biopsy is required. Removing the entire lesion, plus about 1.2 inch of normal looking skin around it, makes sense if it can be done. This procedure allows a specific diagnosis and therefore specific treatment. If is also the principle treatment for single lesion cancer and chronic bacterial/fungal infections.
It sounds like the vet you used suggested an appropriate procedure. She tried the less expensive method of treatment without a diagnosis and said that if it didn't work, a diagnosis was needed. My guess is that she is competent to carry through on removing the lesion and appropriate treatment.
If you still want a different vet, ask friends with pets who they recommend and why they like the vet. Choosing a vet is similar to choosing a personal doctor. You should find someone you like and who can explain what is needed and why.
Let me know if you have follow up questions.