Hi Catsplus2-
I flew internationally out of Chicago two weeks ago. For O'Hare (notorious nightmare) we were there 2 hours and 45 minutes with 2 adults and a very well-behaved 11 year old and we didn't have extra time to "lounge". I would have been rushed had we gotten there any later.
But it depends on your airport. 10 years ago I flew out of Oklahoma City to London Heathrow and I got to the airport (not on purpose) 45 min before my flight. But that's a smaller airport and there was almost no one there at 6am, so we didn't have any problems. It was just me and 1 other adult - no kids, so that makes it quicker. And we followed all the "rules" so it was pretty quick to check in and get through security.
A couple things....
1. Find out which terminal you fly out of - for many international flights if you are on a domestic carrier you won't go out of the international terminal (we did, but my mom flew internationally to Mexico the month before and flew out of the regular terminal on United). If you are flying out of Sky Harbor I don't think there is an "international terminal", so it would just be the regular terminal for your airline.
2. Boarding for your flight will be no different than any domestic flight - you want to leave the extra time because many times international flights are larger, so there are more people and it takes longer. Also, many times you have visitors returning to their country with extra forms (VAT /tax refunds etc) which will also take longer.
3. As another mom said you have to have your passport. This will be for ALL travelers, including children (and infants). And typically your passport has to be valid for travel in the next 6 months (can't expire before then).
4. Security is the same security you would go through for a domestic flight - no difference, even if you are at an international terminal. When you arrive in Canada you will have to go through customs - they will give you paperwork to fill out on the plane. Depending on how old your kids are they will have to answer for themselves to the customs agent (which can add time on that end) - just basic questions... how old are you, where do you live.... that sort of thing. Although the guy in Bali did ask my 11 year old if she's been sick with the sniffles at all in the past month. Luckily she knew to answer no!!!!
5. You will also go through customs on the way back when you re-enter the USA. You'll get your forms on the plane to fill out and turn into customs agents when you land.
I've only driven to Canada - never flown - but the border patrol is pretty nice to Americans, so you shouldn't get too much static from them.
Have a fun trip!