How can I extend a cable to move an outlet inside a kitchen island cabinet?

Due to remodeling, I need to move an outlet in my island. The current system is wired as follows: a 12/2 NM wire comes from the circuit breaker box to the first (non-moving) outlet, and a 12/2 wire runs from there to the second outlet. I can't just direct this wire to the new location because it is too short to reach. Also, there is not enough slack to pull the first outlet out to connect a new longer wire.

Therefore, my plan is to cut the wire from the circuit breaker and route it to a junction box. From there, I would run a longer wire to each of the outlets. I tried to verify this was to code, and came up with some questions (everywhere I look for the NEC tells me that copyright prohibits putting it up in its entirety, or what I found was so convoluted that I don't understand it exactly):

1. Lots of places have said or implied that you can't put a junction box in a cabinet, but others say that it just needs to be accessible, i.e., not behind a wall or cabinet. Can I put a jxn box on the back wall inside the cupboard where I store pots/pans?

2. Is AC cable required, or can I just use NM? Some sites have said AC is required, but i'm not sure why.

3. Is there a better plan?

Thanks.