Canada, USA and Mexico have similiar laws that covers the situation of one parent taking a child over the border. HOWEVER, Never have I been asked to show proof but I do carry a "blanket" notorised letter just in case.
I have crossed the Canadian/US border about 600 times by car and without a doubt the Canadians are the friendliest border guards I have met anywhere in the world. They are only concerned about what I bought and the booze and smoke thing. This may have to do with the fact Canadian Border crossings are guarded by Tax Collectors (Customs officers) and not immigration officers.
The opposite is true of the US. US borders are guarded first by INS and second by Customs. I rank US immigration up their with the Chinese Red Guards. I have been strip searched, accused of robbing a local vendor, accused of lying and swore at. A few years back when Australians were given Visa Waiver Status, I was one of the first Australians a US immigration officer encountered under the new system. He demanded to see my Visa. It is very difficult to inform a US immigration offficer that I did not need a Visa. He "consulted" with a colleague and he confirmed that I did not need a Visa anymore. The Immigration officer raised his voice - said "Jesus Christ, Everybody is getting in" and threw my Australian Passport over the counter to me. Welcome to America!
Yes, what Empress says about HNL is true. US INS officers do indeed check your passport if you are "transiting" between flights from Canada to the South Pacific. I assume this is because HNL airport was never originally designed as a secure transit airport. I think they believed that if a passenger got off in Honolulu then it must be the final destination. Heavens forbid an Aussie may actually change planes on the way to Canada or vice versa.
It is all a mute point anyway. I have always argued that immigration entry controls are useless if there were no mechanisms to keep track of who actually left. Canada gives out 90 day entry permits but it does not keep track of who leaves. The US gives out SSN to temporary workers but it has no exit controls that would keep track of who overstays their Visas. The system has many holes in it.
Now if only Toronto Airport can get their act together and combine USA arrivals with International departures with a secured transiting area. That bus ride in the middle of December between terminals certainly does not make Toronto an attractive hub!
Merry Christmas Y'all