No, I don't believe that you were being "too strict". If you needed to let someone go due to aggression, that is a safety issue, not a personal belief conflict. And if the second mom had issues with you not allowing the bottle, and with naptimes, then she will probably find that a nanny may be a better fit. I would have said the same about the bottle, and explained it as a health and safety risk. It's not because I am judging this parenting habit, I just can't have milk dripping all over a playpen, etc. Naptime is NOT negotiable in my care, either. She will likely notice that it's the same with most group care arrangements.
If things are explained properly (as I am sure you did!) we can get on the "same page" as parents without making it seem like we disagree with their parenting, or are telling them to do it our way.
I think you just had a bit of a rocky start. Good luck moving forward!