I have to go with overreaction as well. Considering he was still inside the vehicle, probably twenty or thirty feet away from DD, and said nothing more than, "Hey, do you want some ice cream?" in his capacity as a known ice cream vendor, I think this is reasonable behavior.
Certainly I could see someone being bothered that a stranger (though not really, this is his regular route) spoke to their child when an adult appeared to not be present. But given the entire circumstance, I think appearing and saying, "No, thank you, no ice cream for us," would have been sufficient. You could even have said, "No, thank you, we don't eat ice cream, so no need for you to ask again." Raising one's voice, implying an unsavory accusation, and ordering him to never come back seem a little over the top to me.