Best of luck to you - ya never know, maybe this meeting is just to clear the air and clarify schedule/policies etc., but doesn't sound like it.
As far as recording the conversation, you need to be careful again as to what the State Laws are - in some states you cannot record a conversation without both parties being fully aware they are being recorded.
For a letter of resignation, esp. if it is the owner of the company you have a problem with, I think it's pointless to air your complaints. If you do choose to resign it's often better to cut your losses and not burn any bridges. Networking is the best way to find a new job, you never know who knows who, and who your former employers knows. I think it's preferable to simply state you are resigning from your position and offer two weeks notice. You are under no obligation to state the reason for your resignation. If pressed you can state that you feel it just isn't working out, the hours/days you were required to work were different than what you were hired to do.
Did I read correctly that you've only been there for a few weeks? If so then it's doubtful that you've been there long enough to be eligible for unemployment if you were not working elsewhere prior to this job, but as every state varies, it never hurts to file with the State unemployment office. Ya never know, you just might find a new job that way.
again, best of luck to you. There are good bosses, there are bad bosses, unless you are having trouble affording food and rent, life it to short to put up with that sort of disrespect. Hopefully the next boss will be much better.