You aren't doing anything wrong.

It's really tough when they know what they want but don't have the communication/negotiation skills to ask/understand.

Explaining anything when they are doing that is futile in my experience, so what has worked for us thus far is simply saying "I am not going to tolerate that behaviour' in a moderated voice and me putting them in their room. Not as punishment but because it's quiet and child friendly. I tell them that when they're ready to calm down, then I'm happy to deal with them.
Usually within about 20seconds it's over and she's found something else to do than tanty. From about that age DD would say, alright mum I'm ready now....
Out and about again I say that and she goes in the pram/ or we return to the car.