H.W.
To stick with the first question: no, I do not think that I know better than a posted sign.
Actually, I am a stickler for obeying signs right now. I have a five year old in tow with me most everywhere. I used to jaywalk like a fiend, but now we will not cross unless the WALK sign is on. I am the example for my son. This means sometimes that we don't play in public fountains everyone else is playing in-- because the sign says no. (BTW- some of these fountains have recirculated, disgusting water and drop-offs, so there are health and safety reasons to avoid these places.) This is hard on Kiddo, sometimes, but there are also good reasons to obey those signs. He will learn a sense of discretion when he's older; right now, I need him to know that the letter of the law is what should guide his actions. And if I am modeling disregard for signs and notices, I would expect that he would also choose not to follow those posted rules.
In regard to the two situations you listed: what a toss-up about the bear/dog/gun situation. Because of the ambiguity of the converging laws, I don't really know what to think. As for the mother-- yes, I do believe she was negligent. We also have to factor in basic questions like "does she have an intellectual disability?" and "can she read sufficiently?" If yes, then I am so sorry to say, she was horribly negligent. What a tragic consequence.