Differently?
If it was me I may have simply said
''Hello Mrs Smith, I am ever so sorry but I have a minimum charge of £10.''
No explanation of the time taken setting up as it may come across as a bit condescending.
If she still replied the way she did I would permanently delete.
that, is the right answer!!
I think the op handled it very well, but from experience these types of customer just feel agrieved and the longer version where you try to be reasonable don't work - are you sure you couldn't have found the time to go back?
As for locked gates, if it's locked and needs a key then we don't go over, we'll happily draw a bolt and re lock after but no climbing over as many gates are in a poor state and climbing on them will only add to the wear and tear. Also many customers have said and I've gained a few too that if it's locked stay out, previous windy has ignored this and now no longer clean the property.
As they say nowt as queer as folk.
Put it down to life's rich tapestry, hold no grudge and move on..
Darran