I relocated back to the UK from Australia last year and shipped my two dogs so I do have recent experience, although, I don’t know Canada’s regulations but I certainly wouldn’t recommend long haul for a dog for a 4 week holiday.
It is too stressful, there are so many regulations and paperwork involved and if there is a slip up in the paperwork the dogs won’t be allowed into the country, which could incur additional costs, boarding etc., It would also be a very, very expensive to do. There are not only the animal flights, vet checks (ours had to have rabies injection and we had to wait a month before they could fly, there are sometimes other tests that are also required, paperwork preparation etc., IATA approved travel crates to be purchased or hired (airlines have strict rules on these in relation to size of the animal (again the vet checking the dogs prior to flight can refuse to release them). For importing clearance of the dogs at Heathrow ARC was at least a 9 hour delay before they are released. I used an animal transport company but it was still very stressful for me as well as my dogs.
I would recommend a good kennels, or a pet sitting service. You could check at your vets for recommendations.
When living in Australia and I was visiting the UK, my dogs were in a kennels and the owner would take short videos of my dogs and put them on her facebook page so I could see they were okay.
Hope this doesn’t sound negative and off putting.
Good luck I hope you find a satisfactory resolution that works for you.