<human>: Can you give me the gist of the text in a nutshell?

I went to see someone in their local office and brought everything I needed including W-2s, 1099s, HSA information, charity donations and student loan interest statements. The person who I worked with was old and slow, but I assumed it was just a learning curve with the system. I had the appointment and then didn't hear from them for days until I called and complained, then the returns were officially filed.

They were correct on my federal refund, which I did receive. I was told because I was a New York and a New Jersey resident in 2014 that I had to file two returns for NJ, one as an in-state res and one as an out of state res. (My job which I had the entire 2014 was in NJ) Here is where things go wrong.

They told me I owed NY, which I promptly paid ~$500. A few weeks later I get a check in the mail from them for $300, I overpaid. They told me I'd be getting two refunds from NJ, I received the first one as an in state resident for $200 ish and have been waiting on the second half. I filed in February and still to this point had not gotten the second check estimated at $160.  

This week, I get a bill in the mail from NJ saying I owe $275. Something was clearly done wrong. Secondly, why would NJ give me a refund in the first place if I was going to owe? I am furious and have an appointment with a different HR Block rep for later this week.  At this point, all I want is for the $250 fee I paid to have my taxes done refunded. Everything that could have gone wrong has.

What are somethings I can say or ask for to ensure this happens?
<bot>: HR Block miscalculated what I owed NY so I overpaid then got a check back. Miscalculated what I owed NJ, got a check back but now have gotten a bill for NJ saying I owe more.