David, I believe that for you to ask the question in the first place, you regret losing this customer and know that if you could have handled it differently and kept her custom. She was on first name terms with you, and in my book that gives you some value in her eyes.
For my twopenneth, I always try to provide a service which pleases my customers, which sometimes means sacrificing my own feelings to a degree, but sometimes it may not be possible.
In the situation you describe, I would have either climbed over the gate if safe to do so, (always with said customer's permission beforehand), or simply done the fronts and charged accordingly. If it were reasonably possible to go back as requested to do the backs, I would have done so. If there were genuine reasons for me not being able to do so, then I would have simply said that I would be in the area again in x number of weeks time and will give them a doubly good clean then.
My feeling is that she would have probably accepted that and you would still have her as a satisfied customer.
Best wishes,
John