I would also say that London, Ontario is (or can be) walkable. Old suburbs are close to the city centre, and the leafier, newer suburbs are walkable to 'outside town' malls. We are 5km from the city centre, but walkable (800m-ish) to some big box stores, including bars and restaurants.

Hamilton and surrounding suburbs are mainly walkable - or you can use cycle paths (and there's great public transit - bus network within the City and trains and coaches out to Toronto).

It was a dozen or so years ago now, but I moved over on an intra-company transfer with a Temporary Work Permit (TWP); the company paid reasonable relocation costs, and although they didn't specifically sort me out with flights back to the UK, they were reasonably accommodating of flexible travel plans that included breaking journeys in the UK for a few days every now and then.

For what it's worth, my experience with your questions was:
1) Typically, for an intra-company transferee in the senior management or specialist knowledge category, an accompanying spouse will qualify for an open TWP so can work for any employer in any location that is not otherwise restricted (from memory, healthcare and education would have required additional screening).

2) My eldest (now a stroppy teen) was just starting out in the school system, but all other advice and second-hand experience seem to boil down to this: if you know you're only here for the two- or three-year rotation, then try to persuade the Powers That Be to put your kids in the equivalent to the year group they'd be in in the UK. If you plan on staying long-term, then it's almost certainly more sensible to have them join the appropriate cohort for their year of birth (the Ontario school year runs Sept to June, but the age cohort is based on calendar year of birth, not age on September 1 as it is in the UK). Most elementary schools have some sort of arrangement with third-party providers (often the YMCA or similar) for before- and after-school supervision.

3) I worked for several years on the borders of Markham and Richmond Hill. There are halfway decent areas in both, particularly in the old centres of RH and Unionville, but an awful lot of vast acreages of tract housing (dbd's characterization of "Basildons to the limit of your imagination" is not altogether hyperbolic) in between. There are semi-rural communities east and north of Markham, but bear in mind that the idea of a small market town isn't quite the same here as it is in the UK, and you'd likely need to head by car to a major centre for anything but the basic essentials. You'll likely also struggle to find good transit links to downtown Toronto away from the Lakeshore GO train line or one or two other dormitory corridors served by GO, but that puts you right back in suburbia again.

4) can't help you there. Our dog is from here, via a rescue agency

5) As I mentioned, I didn't negotiate flights separately, but I had a few work trips to Europe that I was able to tack time onto the end of. I suspect a bigger consideration will be whether you have the time for multiple trips back to the UK. While you may be able to negotiate decent vacation allowance as part of your transfer, your OH will likely start with fewer vacation days than you've been used to in the UK; you may not wish to squander these on long-haul trips. I'd work more on persuading your parents to come out to visit you: their time is more flexible than yours!

HTH

One strives for the essential truth expressed in a pithy manner.

Just something to think about Anna - my wife and I spent 14 years in Canada, and returned to the UK earlier this year. Our parents made frequent trips out to see us in BC over that time, our own holiday allowance and the nature of being self employed meant only 1 trip back for me to the UK.

As time went by our parents ability to travel (and afford travel/health insurance once they were in their 80's) diminished, to the point that they were no longer able to physically make the journey. We ultimately had to make the decision to move back to the UK to be closer to them and help with their care.

The cost of relocation is substantial. Aside from shipping and flights, when you factor in exchange rates, realtors fees, stamp duty, replacing cars and many expenses you wouldn't have had if staying put, it all gets a bit eye-watering. Finding work again after a considerable time out of the country has also proved difficult.

Go into the move with your eyes open, and realize the potential upheaval and cost should circumstances change.

Not Tetsworth by chance? A friend of mine used to live there but is now in bucolic Parslows Hillock.

I'm heading for 3 or 4 days in the Hamilton area just after New Years to a definitely and proudly not walkable community just outside of Hamilton proper. The area near McMaster and much of Hamilton beneath the mountain is quite walkable.

^^^ These are good points.