Of COURSE YANBU. The woman sounds vile.
You should have said 'go and report me to the store manager if you think I am in the wrong. Better still, call the police.'
I know someone this happened to. She got screamed at by a huge 30-something male, for parking in a child zone even though she has a blue badge, (because there were no disabled bays.) When she said 'I am disabled' he said 'you don't look it, you just look fat, you stupid cunt.'
She saw a security guard coming over (as he had heard this bloke's loud booming voice,) and told him to go fuck himself, said the baby in his car was probably not his anyway, and that his wife looked like a dirty bitch who fucks other men.' He went cataclysmic and she just laughed at him. He screamed 'I will fucking kill you - you old cunt!' 
The security guard heard only HIS outburst, and charged over. He accosted him, and threw him off the property; banning him and his wife from the store.
This woman I know didn't exactly behave impeccably, but he started it, and got what he deserved. Shame about his wife as she probably didn't deserve it.