I agree.
"Storming off and leaving the job" is hardly ever considered the way to go to be approved for unemployment benefits. When presenting your appeal in the hearing, I would avoid any such picture. Show that you felt you could do nothing except resign. Stay far away from the "stormed off " scenario. They will always ask if the claimant has exhausted all reasonable alternatives to quitting before they leave the job by their own decision. Behavior that is reasonable, professional and unemotional is at a premium. Having your pride may be fun, getting in a huff and walking off the job may give you a warm glow for a few minutes, but it does not win appeals.
It was not strictly necessary to the performance of your duties that you tell anyone but the manager about the owner's girl coming in and picking up beer, was it? I don't understand why you and the owner had such a fuss about this issue. Were you threatening to call the police on them? I mean, you might have concerns about your liability for an underage person getting the beer, though you technically did not sell it to them. This was a legitimate issue to discuss with the manager. And you might have concerns about the loss of inventory, and have that to discuss with the manager (two cases of beer are gone here, no money in the register for them.)
But why would you find it necessary to discuss that with anyone else? Who? Before my hearing, I'd do some research with law enforcement in my area about exactly how much liability you might possibly have had, what would be the correct action to take about the situation before my hearing, so I'd be able to explain this to the appeals officer. You don't necessarily have to tell them exactly what happened, but you can certainly find out the answer to a general question about selling beer to a minor vs. having knowledge that a store owner allowed a minor to take beer out of their inventory.
I also agree with cbg in that you have absolutely nothing to lose by filing an appeal of this initial decision in a timely manner and continuing to certify for weeks that pass. I would be looking like mad for another job, with the pretty strong assumption that I might NOT be approved in appeal, and unemployment benefits was something I could not count on, but as long as you are not working, have the time and all, why not pursue this?
The owner may not want to put the spotlight on themselves after this very hinky behavior to the point that they do not even show up for the hearing.
If this is the case, you will still need to attend the hearing yourself, even if you are the only one there, you will still be required to give your testimony. Whether the other party shows up or not, you will need to strongly emphasize your concerns that you were being asked to do something illegal, that you might be legally liable for the minor taking the beer from the store if you did not notify someone, that you felt the best, most honest performance of your duties required you to inform the manager, and that you had certainly never been told what to do or who to tell, or that there was any policy to be used in this circumstance.
You would aim your dialogue in the appeal as that you tried to be reasonable and mature in your talk with the store owner, that you told them that you were doing your best, that you did not want to lose your job, but that it became obvious that if you continued to work there, you were going to be expected to agree to cooperate with these sorts of little forays by the owner's family members, legal or not, and that because of this, you decided that you would rather find another job than stay around and be complicit with these actions.