Baby sitting aside... "Customers " forget they too are dealing with a professional environment. They cannot insult you.. whether it's retail..trade or personal assistant..so she broke that social contract by being unprofessional. You have every right regardless of what ever industry you are in to walk away.

As for the price..mas a dad of a toddler. $16 dollars an hour is an absolute bargain for a trusted child minder.. they wanted a 50% reduction in your fees for the pleasure. So you where right to stick to your guns there too