I agree with Nelle about impulse control - I see it with DD all the time. Yes, they are often old enough to understand, but their brains are still developing and controlling the impulse they have to touch (even when they know they're not supposed to) comes later for some kids.
Personally, I am regretful of having used the word 'no' so much with DD - it is her favourite word now. I hate hearing it from her so now I sort of understand how it feels for her to hear it so often from me. If I could do it again, I'd make sure there wasn't so much stuff around that I didn't want her to get into. JME. GL finding common ground with your DP - you are right - it is important that you are both on the same page.