This is one I'd certainly let the unemployment system get in there and hammer out. It could be argued both ways, though I suspect this OP would jump quickly and proudly onto the "I quit! I gave two weeks notice!" bandwagon and thus completely talk his way out of unemployment aproval. This will suit the employer just fine, as the claim will be denied, and they'll be off that particular hook. They wouldn't likely argue with anyone who said the employee was giving two weeks notice and was told to go on and leave after additional problems and issues surfaced.
But as I said, since this was a part time retail job, and we don't know about how much this person had worked in the past 18 months, if there aren't enough covered wages to make up a claim monetarily, they won't even get into these separation issues. I feel that this is a case of the OP being really over-involved in some workplace drama and believing there were more rights and protections for them on the job than there really are. You have the right to quit, and they have the right to fire you.