This is the way i would be looking at it.
The job takes 10 mins for £12. On a good day thats a nice hourly rate.
Youve wasted probably 10 mins just on this forum debating what if not longer and your not getting paid for that. If you go back and see her try and reason with her then maybe offer a reclean thats probably another 20 mins wasted plus 10 mins driving there. When all said and done you might waste 1 hour+ for the sake of earning £12 for a customer who sounds like an absolute nightmare from the get go.
I have learned to go with my gut feeling and let the universe speak to me. If a customer looks really problematic from the start, do i want to waste my time and self respect to try and convince them of my worth, or am i better off to just use my time to make more money for other customers out there who will respect the value in my service.
I used to get so upset with non paying customers or complainers. Now i just dont care. Bin them off, onto the next one. Always be polite though and if anything apologise. Do this purely so that they dont leave you a bad review. I couldnt care less about there feelings i just dont want a bad review online from a psycho karen type customer.......
I've had the same issue as you in the past so i can totally get how you are feeling ive had it myself many times in the past.
If you are a man of principle then take her to the small claims court. I am no longer a man of principle. I dont care if customers dont pay me, i just want an easy stress free life that doesn't involve threatening to take customers to court for the sake of £10 lol.
Dont need the stress, im happy to bury my pride and principles for the sake of an easy life and easy money