I had a bad experience during my NAUI certification, and the other dive shop in my town is PADI. Would it be stepping on toes if I were to redo my certification thru the competitor shop? What other options do I have if this is the wrong choice?
No issue whatsoever. If the previous instructor couldn't teach you well, then no reason not to look elsewhere. It could have been a poor instructor, or the style was just different.
I also have two Open Water certs. First was through PADI, second is YMCA, but instructors were also certified with NAUI and CMAS, so I could have gotten those certs as well during the course. Figuring I already had the PADI cert, I saw no reason to get 4 OW certs.
In my case, my first instructor was definitely poor, and the course did not meet standards. I left that class with a OW cert, a decent grasp on the academics, but not much confidence in the underwater portion. So, I figured it would be a good idea to do the course again.
Depending on what you need as far as instruction, you may be able to complete just a refresher, with a different instructor. Definitely worth talking to them about your previous bad experience, and what you feel needs work, and they may recommend something short of full re-cert.